You definitely cannot check in the dark. If you do, you are playing the next hand with no knowledge and it could prove costly. Betting now saves you money on the turn of the river should it turn out to be unfavourable.
Bet 60% of the pot in that situation. You need to lead and show strength. It is such a wild assumption to put your opponent on trips or a straight off the flop. You are the favourite here. If the opponents fold, so be it, just take down the pot.
A pot sized bet is negative -EV in the long run here. 66% of the time your opponents don't hit. Betting 100% or 150% of the pot is a losing play.
This is how I would think.
If the big blind is a smart player at all, he is re-raising if he has AA or KK and maybe QQ after that min-raise by the button. He wants to isolate one of you because then he is a clear favourite. If he isn't re-raising then I think his hand range is anywhere from AJ+ or perhaps KQ, but unlikely. But, it is low level, so he may be stupid and may have KQ out of position, or even AJ.
With the button, have to take into account his position. Although he has re-raised, his hand range is still rather large. In honest, I re-raise on 6 handed even with suited connectors at times, he could be on anything. He however is the player you have to worry about, not the big blind. He is the one with position.
To sum it up, lead out, bet 60% of the pot, if he re-raises I would fold. If he doesn't and just calls, fire another bullet at the pot regardless of the card. Maybe a 50% bet of the pot. He might be scared you have the straight. If he calls, you know where you are at, and you get out of there.
Plus you can always suck out and make some money.
But kind of hard to judge without a read.
Just curious, what does everyones notes on other players look like?