This is something that Guy says to Millie when he is trying to describe why he does not feel contented. I believe that it is somewhat of a metaphor. He is doing two things. First, he is saying that he does not feel content and comfortable. Second, I think he feels like he is more weighed down by things than he had been not too long ago.
When you start to gain weight, you don't really feel comfortable. If you are aware of the weight gain, you feel more sluggish and your clothes don't fit and such. This would make you feel discontented and upset. I think Guy feels this way.
More metaphorically, I think that Guy feels weighed down emotionally. He is starting to care about things he didn't care about before. He is starting to think. The thoughts he has are pressing down on him in a way that he has not experienced before. I think that this, too, makes him feel fat.
Montag feels "fat" because his new knowledge of and interest in books is a great burden. The burden is so great that it is even effecting him physically; he feels uncomfortable in his body, and he feels heavier. Obviously the burden of his new knowledge would be great. There is a world of knowledge that he is obsessed with exploring, but greater exposure to that world depresses him because it allows him to see more clearly exactly how horrible the society he lives in is. The sight of Mildred, her friends, and other supposedly "normal" people fills him with anguish and frustration. He is worried about what he feels he has to do to shake up this society, and furious at the blissful ignorance of everyone around him.