I'm sure some gay men might prefer dating overweight or obese men, they usually call themselves "chubby chasers". I don't think there's a way to know what percentage of gay men would prefer that body type over someone in shape thought.
When it comes to escorts they're are usually prepared to deal with men of all ages and sizes, specially in the USA and not so much in Europe, whether they're attracted to them or not. It would be nice for clients to accurately describe themselves before an encounter, I've read in RM many clients profiles describing themselves as "chubby" at 300 Lbs.
I remember ads saying "in shape only" but I haven't seen those lately because some potential clients consider them to be a turn off.