25 isn't too young, and makes sense if you have focused on education and career. I followed a similar path in that I spent a lot of time in education, only starting to properly consider courting someone around the age of 25 or 26 after I finished my PhD. Things were complicated somewhat by Covid, but I got married last year at the age of 30.
As to losing weight, I can't speak much from experience on that, but losing some weight may be a good idea, as much for your own health as anything else. Unless you are really overweight (in which case it is a medical issue that you should address), I think you shouldn't worry too much about it in terms of dating.