Amos Hart is Roxie's poor gullible sadsack of a husband. Depending on when you ask her, he's either her "funny honey" who "follows 'round like some droopy-eyed pup" or a "scummy, crummy, dummy hubby of mine."
Considering Roxie is cheating on Amos before the movie begins, we see immediately where he rates in her eyes. And is he ever a doormat. He initially takes the fall for shooting Fred Casely in order to protect her. And even after he finds out she's an adulteress, he stands by her side. He helps pay for her trial and everything. His big song is "Mister Cellophane," in which he dresses as a hobo clown and complains about how no one notices him.
"You can look right through me, walk right by me, and never know I'm there."
The lights go out and slowly erase him, even though he gives the song his all. But no one in the audience even registers the performance, or applauds. This is Amos's moment of realization to divorce Roxie: "She probably won't even notice."
Roxie does notice, though… but only when she needs to win him back to win back the court of public opinion. She tricks him into thinking she's pregnant with his baby and that's the reason she shot Fred Casely. But both are lies. He finally leaves her in the end, not that he has any choice. She doesn't even want him back.
But the question remains, why does he stick by her? How does standing in Roxie's shadow so long benefit him at all? Billy always calls him "Andy" and even we barely remember who he is. We definitely don't know what's in it for him, but when Roxie sings, "He loves me so, and it all suits me fine," we know what's in it for her: total devotion.