I wonder if he has already started putting on weight.
ーHe/She has already gotten bigger.
「彼/彼女は早くも太ってきた」
already で「早くも」
to get bigger で「太る・大きくなる」
ーI think he's already started to get fat.
「彼は早くも太ってきたかも」
to get fat で「太る・肥える」
ーI wonder if he has already started putting on weight.
「彼は早くも太ってきたかな」
I wonder if ... で「…だろうか」
to put on weight で「太る・肉がつく・体重が増える」
ご参考まで！
カナダ 
