Top Two against a nit LIVE 2/5

[e_hammer]

2/5 live
Stacks effective $500

Button (Villain) seems to be a total nit.
Never raising and only limps pots until makes something
substantial before putting much money in the pot.

Villain open limps button
Hero - Raises to $25 in SB (A Q offsuit)
Villain calls

FLOP Q T 4 rainbow

Hero bets $40 and villain calls

TURN --- A placing 2 diamonds on board

Hero checks, Villain bets $90

Hero??

Note: Hero thinks that he should not have checked, however that is another topic. As played how should we proceed?