villain 91/66 over 12 hands

$1/$2 No Limit Holdem
6 players
Converted at weaktight.com

Stacks:
UTG gamesman09 ($177.10)
UTG+1 Phwap ($200.00)
CO GunTucker45 ($159.75)
BTN GeniusEC ($200.00)
SB mjrnt ($221.70)
BB Hero ($348.75)

Pre-flop: ($3, 6 players) Hero is BB
gamesman09 raises to $8, 4 folds, Hero raises to $24, gamesman09 calls $16

Flop: ($49, 2 players)
Hero bets $26, gamesman09 calls $26

Turn: ($101, 2 players) Hero...checks?


Was talking this hand over with some tosser last night, and the tosser was saying this villain's range is too weak to handle two barrels, so a check is good here. Conventional wisdom is zomg overpair + donk = keep betting till the money's in the middle, but his range is very weak so maybe we should be checking to induce, or to get more value from his underpairs on the river.

That being said, I really wanted to play for stacks here and felt like I had to bet the turn to setup a river shove that wasn't an overshove, also I didn't really know anything about how v played postflop -- if inducing was even worthwhile. I think we've all seen bad donks call three streets with underpairs in worse spots than this, but maybe that frequency isn't high enough for all 3?

Is this all just a whole lot of overthinking of a standard spot?