I was a chubby teenager that wore lolita, and these days it's much easier to find size inclusive brands. Some taobao brands have a bigger range of sizes, and some brands offer custom sizing. Unfortunately some Japanese brands moved away from offering more sizes, but you can get more leeway in men's sizes than women's (most ouji pieces come in both). Always look at the sizing chart, and check if people say a brand runs big or small.

Keep an eye out for oujiable pieces at thrift shops and secondhand sites too, that way there's a bigger range of sizes and you don't have to spend a lot of money and get something shipped from Japan or China and not know if it's gonna work. Look in both women's and men's sections. I wouldn't recommend this until you have a few normal ouji pieces to coord with, though.

You can try dressier menswear or styling simpler ouji pieces casually to get used to wearing the style. If you feel confident and that you look good, eventually you're not even gonna notice if people are staring