Looks to me that the BB had two diamonds with the 6

pushing a diamond flush and an open-ended str8 draw. With all the betting he could put one of the players on a set and cool down completely after he not only missed the flush or draw, but also saw the board paired. Saving a bet at the end there does make some sort of sense if he has his oppontnets tagged as being non-bluffers.
Might have had A

6

, which can be pushed a bit more preflop five-handed.
Just a guess of course, but it fits.
Have you calculated your odds versus a set? You are a 74% dog against top set of 7's and 66% dog against a set of 4's or 5's. This is strictly a heads up calculation. If you give the other player a flush draw, say A

K

, top set of 7's is a 58% winner, the A

K

is 25% to win, and you are 15%.
Now, only you know how tight and what range of hands are played by your opponents, so you have to guage how likely you are facing a real hand. It is such a big pot you should give your opponents credit for
something, especially at the $10/$20 level.
I can't fault you for pushing an open-ended str8 draw like that but I usually put the breaks on a bit If I get a lot of resistance, because it is a good hand, but not a great hand, when you consider how you stack up to other playable hands
When the flop has a flush draw, you know the str8 draw with 6

6

is roughly 50-50 with a flush draw like A

K

and you are just feeding the rake for a coinflip, though it can be argued the rake is maximized anyways if the betting is wild. Sure you will be happy to win a big pot but you understand that 50% of the time you are losing a big pot. You are just feeding your variance here.
Then there is the fun times when you make your str8 but also allow the flush

.
If you have this open-ended str8, but you are facing an overpair such as 88 or 99, you are a 25% dog.
As long as you are getting the odds, it is ok.
Thanks for posting this hand and good luck in your games.