It does appear to be a contradiction for games on this site. The ones with robust fat content lack explicit sexual content and vice versa, like they’re opposite values on a slider or something.
The ones that seem to tread a fine middle are Gumia’s Unbelted Terror (More weight focused but there’s a lesbian sex scene in the first town), Hungry Girls by Paploman (More for expansion fetishes in general than just weight gain and it’s also a grindy-as-hell gacha trap), and Free Cities (A open source text based slave owning simulator with a limited weight gain mechanic, but very robust romance and sex options)
One project that I’m very much looking forward to is Love is the Way to my Heart, which is an upcoming text based weight gain dating sim with art by GentleGolem that looks like it plans to have explicit sex scenes written for it.