Playing the river out of position with medium/weak holdings

There are at least 2 schools of thinking.

1. You shouldn’t miss bets - every time you checked and then call a bet, you should bet in the first place, because if not, you are losing the value of weaker hands that would call you if you bet, and only check behind if you don’t bet.

2. Checking, you are playing with all the range of the villain – that range includes all the possible bluffs that aren’t present in his calling range.