Middle Pair on the Flop

This is one of the trickiest spots in multi-way pots. You hold

8 ♣ 7 ♣

And the flop is a dry:

4 ♦ 8 ♥ J ♠

You're on the button and it's checked all the way around to you.

Do you bet? If you do, most of them will call. They'll call with AK, J6, 76, T9. They're calling with outs, and it's hard to tell what the next card does for them.

I ended up betting this, and going to the river with another player. He showed 89o and took down the pot. Should I have checked? I'm not sure. Then someone would have bet at me, and I'd be stuck with a decision: are they betting K9 on a bluff, or semi-bluffing w AQ? Were they looking to check-raise on the flop and missing?

Just happened again with a similar set up:

I hold: Td 8c

Flop is:

Ad 8s 6c

I'm OOP so I check and it's checked around. If someone had ace, they'd let me know, so I feel good. Even better than the turn is Td. I've got 2 pair and someone will call me. I bet and get two customers. But the river is: 6c. I bet and get raised. He turns over 36d for the busted draw that hit the river. Again, a probable check-the-river situation that I missed. It's easy to get excited when you have nowhere near the nuts on the river...