I'm all for pot control with big pairs, but not against a guy I know is capable of making this push when I don't know what it means. You checking that turn screams AK or AQ and could lead him at 77-TT and that makes a lot more sense for his riverpush than the "desperate push for value." This really looks like he doesn't wanna get bluffed off his hand to me.
He's a sLAA by your read, so I'd throw AA-TT out the window because I think he shows some flop aggression with these hands. You don't know where 11 of the clubs are, but I think he shows some flop aggression with a club draw as good as King high.
That said, what beats you in his range?
, 33, 44, 66, and 57.
What do you beat in his range? 77-99, 55, 22, and AJ/KJ/QJ/AT could float this flop and check the turn. Busted clubs are another option, of course, but on a smaller range, IMO.
I'm guesstimating that you're 2.5:1 against my range on him from your prior read making this a +EV call by ~$200'ish. Still a tough call, cause it's so much.
But what do I know, I'd bet $55 on the turn. Pot control isn't just checking the turn, it's having the control and against a guy that you KNOW is heavily capable of taking that control away from you OOP, I wouldn't check this turn without at least a set to this board or complete air. I'd check 55 and a big flush draw, too. But I'm betting AA-QQ, TT-77, 67, 56 and any Jack here.