[brazilio]

This would seem to indicate to the opponent that when you check, you've got something more often worth getting involved.

For instance, say you fold 30% of the time at some random board when he bets to you but you open fold any significant percentage of time within that 30%, and you have another action the other 70% of the time c/r, c/c, what have you.

That would indicate to me that when you don't open fold, it's more heavily leaning towards you getting involved in the pot even if often you're going to be folding to his flop bet.

Getting the free card might make it worth it because it more clearly defines his hand as weak. At the same time, his flop bet when you check also more clearly defines his hand as strong(er).