Villain: btn steal is 54, fold to cbets 62% in 3bet pots after 11k hands, wtsd 42, fold vs cbet flop 58 turn 42 river 80

I prefer to 3bet this pre due to villain overfolding post + T977 should have some deception and mid flops playability.

Flop cbets or check is i think close. If villain does not like folding turns/rivers and isn't agressive i think i would prefer to check and usually realize my equity (because of how often i hit this flop i would not expect to see him betting often). In this case I think I like cbetting better, because we can make loose barrels on turns/rivers, because how strong our range is (assuming villain takes this into consideration) and villain overfolding. His river range I estimate to be A+draws (flush/straight), 2pair (A9/A5/AK/J9+draws, AJ would often shove turn) and QTxx (AQT,KQT,...). I think 55/99 would usually shove turn as well. River card is pretty interesting, because of how strong my overall range is at this point.

What our range play should be? 
I think with straights we should be potting it so we can polarize ourselves and narrow our value range, we add bluffs for balance purposes. How should we procede with JJ+ (i assume we are checking with AK-) ? If we bet big, for example 110 i think our perceived range is too strong for villain to make many mistakes (should we bet smaller? if we pot our entire betting range i think we will not have remotely enough bluffs to balance our range).