Approach to playing mid-pairs

This is a general question because I found through some hand analysis that I am losing a lot of money playing hands like TT-77, particularly in 6max.

Here is one example playing 5/10 NL on Party 6max. All relevant parties have stacks over $1000. Folded to me on the button with 88. I raise to $30. SB completes. BB folds. Flop is JT5 rainbow. SB checks, I bet $50, SB calls. Turn is a 4, SB checks, I check. River 7, no flush possible. SB bets $125. I folded.

I am interested in comments on the above hand, but it is really just one recent example of a typical problem I seem to run into with the mid-pairs, which is that my continuation bets are not being folded to often enough on the flop and/or turn to make these hands profitable, and when I show weakness by checking behind, about 90% of the time I face a large bet when the next card comes off.

Does anyone have thoughts on what they have found works when you get the fairly typical multiple overcard flop with these pairs? I admit that I generally raise with mid-pairs when I am first to open, particularly in 6max. Maybe that is the problem, I don't know.