foreign grammar Chinese words... the Chinese language doesn't work this way

你看起来比第一次来的时候胖了很多 is better and sounds more nature.

我们一般这样说，你看起来比第一次来的时候胖，或者你看起来比第一次来的时候胖多了，你看起来比第一次来的时候更胖。

你看起来比第一次来的时候胖了很多。我一般这样说。更多比很多的语气要重，也就是说你觉得对方胖了 much much more。。。That guy will be angry

I would say the second one is better,the first one is not necessarily wrong though.And I don't think it's a matter of grammar,but more of collocation.It's hard to find a reason to rationalise it ,though.I just feel the second one slightly better.Hope this helps.By the way ,your next question is not very clear(I don't know what you want to know the correct option of the choices in brackets or else?).