Butchered bottom set ($100NL, 6max)

[Ojingo]

Villain is unknown but is sitting with 70BB, I cover.

I get 77 in the BB. Villain open-raises to $3.50 from UTG. I'm the only caller.
Flop: [Th][7h]. I lead for the pot, planning to 3bet allin, but villain hesitates a while and flat calls. Turn: .

Question 1) How likely is it that my hand is still good? I'd be surprised if he flat called my flop bet with JJ or QQ; it's possible that he'd flat call with a draw, although more likely that he'd raise that.
Question 2) What's my play? Since I weighed his range towards AK, I checkraised allin here. Very bad?

[Electrolux]

[Twelver]

[k3nt]

[briachek]

[Ojingo]

[briachek]

[T-Rod]