There's a lot of recent evidence to suggest that vitamin D deficiency is linked to weight gain, and with there being such a prevelance of said deficiency in the western world (as high as 50-60% according to some studies in the US)  and even higher in some other countries it stands to reason that for a lot of people vitamin d is good for weight loss.
The question of course is how significant vitamin d is when it comes to weight loss and if said correlation can simply be put down to people who are outside more get more vitamin D, but also happen to burn more calories. 
Interestingly it seems that whilst this was the conventional wisdom for some time, it is not quite that simple. And that in fact getting enough vitamin D is actually related to maintaining a healthy weight. So let's take a look at the potential benefits of vitamin D supplementation for weight loss.
The Link Between Vitamin D and Obesity
Obesity has reached epidemic proportions worldwide, and it is a major risk factor for various chronic diseases such as type 2 diabetes, cardiovascular disease, and certain types of cancer. Interestingly, studies have shown a high prevalence of vitamin D deficiency among obese individuals, suggesting a potential link between vitamin D status and weight gain. 
There are generally 3 schools of thought on why this is the case, and it's likely that all reasons play a part.
- One possible explanation for this association is that vitamin D deficiency may disrupt the normal functioning of adipose tissue, leading to an imbalance in energy homeostasis and increased fat accumulation. Realistically this is likely to be the least important factor. 
- Vitamin D deficiency has been linked to increased ghrelin production (the hunger hormone) and insulin resistance, a condition that impairs glucose metabolism and promotes weight gain.  This is probably the main reason.
- Lastly Vitamin D improves athletic performance, mood and energy levels raising peoples NEAT (the amount of calories you burn through unconcious exersise, which is a higher percentage of calorie usage than concious exercise for most people). 
Vitamin D and Weight Loss
In a clinical trial conducted by Khosravi et al. (2018), overweight and obese women aged 20-40 years were randomly assigned to receive either vitamin D supplements or a placebo. The intervention group received high-dose vitamin D supplementation for six weeks, while the control group received a placebo.
The results of this study showed a significant reduction in weight, waist circumference, and body mass index in the vitamin D supplementation group compared to the control group. These findings suggest that vitamin D supplementation may play a role in promoting weight loss and improving body composition in overweight and obese individuals. 
Vitamin D and Appetite Regulation
Another aspect of weight management is appetite regulation. Leptin and ghrelin are two hormones that play a key role in regulating appetite and satiety. Leptin, produced by adipose tissue, signals to the brain that we are full and should stop eating. Ghrelin, on the other hand, stimulates hunger and promotes food intake. 
A study conducted by researchers at Harvard University investigated the effects of vitamin D supplementation on appetite-regulating hormones  in individuals with type 2 diabetes. The results revealed that vitamin D supplementation led to an increase in both serum leptin and ghrelin levels. Interestingly, despite the increase in both hormones, the leptin-to-ghrelin ratio decreased, suggesting a potential improvement in appetite regulation.
Furhter studies have shown that this applies to none diabetic individuals as well, as have animal studies. [10,11] On top of this overweight populations have a higher rate of vitamin D deficiency, which has in some cases been explained away by a more sedentary lifestyle and less time outside (meaning less exercise in general). However, with what we know now it may be that lower vit D leads to increased hunger rather than a lower exercise rate being the issue.
Evolutionary scientists have also suggest this makes sense, with lower vitamin D levels historically being a sign of changing seasons in the run up to winter, when humans would need to put on more fat ahead of the winter time. As such low vitamin D causing hunger, would make significant evolutionary sense.
Vitamin D and Exercise Performance
While the exact relationship between vitamin D levels and athletic performance enhancement is still being studied, there is evidence to suggest that vitamin D plays a crucial role in optimizing athletic performance. Peak muscular performance has been associated with 25(OH)D levels of 50 ng/mL, which is 2.5 times higher than the recommended minimum. 
Several studies have demonstrated the positive effects of vitamin D supplementation on athletic performance. Ultraviolet irradiation, which increases vitamin D levels, has been shown to improve 100-meter times, increase jump height, reduce pain associated with sports injuries, and enhance strength, reaction times, speed, and endurance. 
When it comes to vitamin D and weight loss, the endurance and enhanced stregnth elements are of course the most interesting, for example improved endurance can mean more time spent doing cardio and ultimately burning more calories.
Vitamin D and Energy Levels
Several studies have shown a strong association between vitamin D deficiency and fatigue. In a double-blind, placebo-controlled clinical trial conducted by Nowak et al., participants with love vitamin d levels and fatigue were randomized to receive either vitamin D or a placebo. The study found that participants who received vitamin D experienced a significant improvement in fatigue compared to those who received the placebo.  More energy means more movement, meaning as we mentioned earlier a higher calorie burn through the day meaning more weight lost.
Vitamin D, Sleep and Hunger
Last up, low vitamin D can cause disturbed sleep, and even a small disruption to sleep can cause a massive spike in ghrelin production. Which in turn makes you much hungrier through the day. As such supplementing Vitamin D or making sure you get enough through natural sunlight can increase weight loss.  For example a study published in the Journal of Clinical Sleep Medicine found that participants with low vitamin D levels had a higher prevalence of sleep disorders, including sleep apnea and restless leg syndrome. 
Vitamin D and Testosterone for Weight Loss
There are also links that suggest adequate vitamin D levels are essential for testosterone production, low testosterone can result in weight gain and increased fat stores in men. 
Optimal Vitamin D Dose for Weight Loss
While the benefits of vitamin D supplementation for weight loss are promising, it is important to note that maintaining optimal vitamin D levels is crucial to far more elements of your health. The Institute of Medicine (IOM) recommends a daily intake of 600-800 IU of vitamin D for most adults. However, some experts argue that higher doses may be necessary to achieve optimal vitamin D status, especially in individuals with obesity or limited sun exposure.
It's also worth noting that Vitamin D has been shown to be safe well over the RDI's and it's quite unlikely that you're going to overdo it unless you're very daft with the supplements. Studies have shown that it's safe and effective well passed the RDI point.
Conclusion: Vitamin D and Weight Loss
Vitamin D supplementation shows some real promise.Studies have demonstrated its beneficial effects on weight, body composition, and metabolic markers in overweight and obese individuals. Furthermore, vitamin D seems to impact ghrelin production, thus actually effecting how hungry you are, improves athletic performance and energy, helping people burn more calories and overall is just a pretty good addition to most people's health overall.
1 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6075634/
2 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3897598/
3 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6780345/
4 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7683208/
5 - https://pubmed.ncbi.nlm.nih.gov/28229278/
6 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7071499/
7 - https://pubmed.ncbi.nlm.nih.gov/30123437/
8 - https://www.ncbi.nlm.nih.gov/books/NBK547692/
9 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8860169/
10 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5921043/
11 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6071442/
12 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3497950/
13 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2912737/
14 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4158648/
15 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8912284/
16 - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6213953/
17 - https://pubmed.ncbi.nlm.nih.gov/21154195/