Trying to Limit the field when I floped middle set

[Tekari]

EP person limped with a few others, I was 2 off the button with 7d7h and called, the button raised, 5 people saw the flop for 2 bets each.

Flop is 6s7c8s

EP bets again 2 callers and person to my right raises. If just facing one bet I was planning on calling and waiting to see what the next card was before raising the turn. To my suprise the person to my left raised so I re-raised trying to get out some of the other people because the pot was getting big. The button folded but the 3 orginal callers all called the additional 2 bets cold.

Turn card was 9d [6s7c8s]. Now I figured someone must have a straight but the pot was so huge. First position bets out, 2 callers and a raise. I cold-call 2 bets. I figured the pot was big enough now that if I got a 6,7,8 or 9 on the turn I would have a full house and extract extra bets from the straights. Someone might have been on a flush draw with the original 2 spades still so a spade on the river could give someone a flush. It is ever correct to fold for 2 bets cold on the turn in this situation against an obvious straight? Turn card was a Q. Middle position bet 2 called I folded and early position called.

any comments? Specifically should I ever give up my set in this situation against 2 bets cold on the river? and people to still act behind me?

Also what about my re-raise on the flop? Should I wait to see the turn card if it's a 3rd to a flush or a scary straight card before raising?