Any info on Villian?

I like the way you played the hand. Betting half pot for value and as a blocker would be okay too.
He might not even raise a hand like KT.

There's more to be worried about than 78. QJ, 6x and KT are very plausible hands here. His bet sizing feels a little polarized, and it's a pretty tough spot.

I think he would bet smaller with KJ/KQ.

My guess is that the GT specialists here will tell you this is a call because AK is near the top of your range, but based on feeling I'd say we're just not going to be good very often here.

Leaning towards a call the more I think about it, but it's much closer than it looks.

Two other factors:

He can't expect you to fold Kx here or maybe even 9x, so I doubt he's going to bluff this board very often.
He didn't raise the flop, so it is slightly less likely he has missed clubs.

I'm calling here. You can probably discount almost all combos of 66 and 99 due to the flop not being raised which leaves villain with what's probably a maximum of 9 value combos (2 combos of K10s, 4 combos of 78s, 3 combos of 1010). Against that range you only need villain to be bluffing around 4 combos to be able to profitably call. I also think that 1010 is going to find a fold on an earlier street some % of the time and that 7c8c probably raises the flop most of the time which means you need even less bluffs in villain's range to be able to call. Finally, this is probably the strongest hand that you ever check here so for that reason I'd also be inclined to call.

We can't talk about his range if there is no information provided whatsoever. Above analysis is all guesswork, you can't discount anything in this situation to a comfortable confidence level really.

Yes it make sense for villain to raise sets/FD's on the flop, it also makes sense for him not to do this. Villain could easily want to get the BB in the pot, since we know nothing about villain we can't discount sets whatsoever.

He can have boats 99, he can have quads 66, he can have trips 67s/A6s, he can have 2pair KT, he can have straights 78s.

So he can have plenty of value combos, your line looks reasonably strong with barreling this turn. And people do not bluff this call call bet lines nearly as often as you think. 

But really with no information no real quality advice can be given.

Keep in mind that the hands you want him to bluff with are:

Axcc, QTcc, TJcc   which also all could have showdown value in villain's eyes.

Given that we need to be good here about 29% of the time, I am fairly confident that you are never good here often enough, specially with no information.