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.
I assume because it is a relatively new city planned to replace Seoul as the capital city to reduce congestion. Its population would be mostly people from outside moving into the area, and elderly people tend to be more set in their ways and less willing to take risks like moving to a newly formed city.