Missed a turn C/R.. .bad attempt?

[JooWish622]

Villain is a maniac, I am still unsure if he is actually good or not. Effective stacks 1k. HU Hero is in the BB. 5-10 NL.

Villain raises to 35 as SB on button, Hero reraises to 110 in BB. Villain insta calls.

Flop is 774 rainbow. Hero bets 175. Villain calls.

Turn: 8. Hero checks?

The reason why I did this was because I thought a large part of Villain's range was a float. But, should I not be looking for Villain to float here in a reraised pot with only 700 left in a 600 pot?

If his range didn't contain floating hands (A4, KQ, 22) this is obv a push and get called by Ak and get rivered, but that's another story.

Or will agg monkeys bet hands like A4 bet this turn sometimes?