This article is a good article to use for this claim. The author sites his sources throughly throughout and the key source used is National Library of Medicine, which is a really good website to cite because it is a .org website, ensuring this article is factual:
https://pubmed.ncbi.nlm.nih.gov/7369170/ - here is the link to that website.
Looking into other websites and claims, they all share the same information that this article claims: caffeine helps to lose weight. Though I would argue it helps to lose weight mostly because it is an appetite suppressor, not necessarily because it increase's your metabolism.
Overall this is a good claim, I would add in more details to further support it but this is a good website to use to further back it.