Translation:He is a little heavy.
かれはちょっと太って（ふとって）います。 Yes, I think I would say so. If this is not talking about a person but an object, I will use おもい heavy. Actually おもい（重い）means heavy like English expresses. You feel the weight, therefore use 重い. When I saw this sentence, I immediately thought it meant 'He is heavy (like always talks about complicated things therefore he is a bit too much)'
Physically heavy can imply heavy due to muscles, bone mass, or like compared to what one was expecting -> picking up a fit Shiba Inu and being surprised that it's heavier than expected. -> picking up a baby who has grown a good amount in a short amount of time -> picking someone up who's a good weight, but you're not as strong in the arms as you have to be.
Many uses for this word that have a meaning we don't think of in English is my point ^^
"Kare" has to be "he", despite your kind intentions. And I don't think this sentence is necessarily mean. If you think about it in the context of picking up a baby or a child, it's just an objective statement. I give my younger Japanese students piggyback rides, but sometimes an older student will want one, too, and when I can barely stand up under their weight, they're not offended by my "omoi yo......."
Either, but if you were bullying someone it's waaay more likely you'd just use a word like: でぶ ふとい ブタ（lit means pig, someone who eats like or acts like one) デクデク（especially when they're running or moving :( ) ぶっとい（do not use this one, even as a joke) むくむく（but this means stature, not always health, i.e. a furry cat could technically be あぶらぶとり