I'm not sure we can get 3streets of value from a worse hand. And i think we're more likely to get 2 streets of value by checking against his entire range.
i thought about checking behind on the turn but figured that if i check and river villain donks..my only option is to call his river bet unless i rivered boat. So i decided to bet on the turn for more value.
I think by betting, many worse hands would call..like 88, A7, TT, JJ...but it's just my two cents. obv when he c/r the turn and shove river, the only hand i can beat is probably Q8