Raising w 2nd best hand on the river

I won an interesting pot today that was a clear example to me about how it is sometimes correct to bet or raise on the river if you think you have 2nd best hand. This idea is described in books like Small Stakes Hold'em or Hold'em Poker for Advanced Players. The situation itself was not unique in any way compared to common examples given in SSHE or HEPFAP, but it is very helpful in the learning process to go through the actual situation yourself to help learn the concept. It really makes it easier to remember when learning from first hand experience.

The general idea is: In a hand where you strongly believe you have second best hand, you should bet or raise if you think that you can get the best hand to fold and worse hands to call.

In this hand, I had the best hand all the way, and I would have folded to the 2nd best hand if he had bet or raised on the turn or river. I made at least 1 mistake in this hand. Please point out any other mistakes that I made.

Hand #1
9 handed $20/$40 live limit hold'em game. All relevent players have plenty of chips. SB has played a moderate number of pots, BB hasn't shown down anything less than a pair on the river and has not made any bad plays so far, LoosePlayer has played very many pots and has cold called very freq w any 2 cards. I have not played many pots and have shown down several very strong hands.
- I open raise in MP+1 w 8h8c (a questionable play but it was folded to me, and the button had a tendency to be agg whenever he sensed weakness and had position. I think my only play is to raise or fold)
- LoosePlayer in MP+2 calls
- folded to blinds who both call
- flop comes 743 with 2 clubs, checked to me and I bet. everyone calls
- turn comes 7433, still only 1 flush draw. everyone checks (my mistake here - I probably should have bet even with the possibility of being trapped - because it was a multiway pot w several draws, pot size 6BB. At least I think so. A clever player might try to bluff or semibluff check raise me, but against non-tricky opponents, I think it is correct to keep betting)
- river comes 74332 no flush. It is checked to the Loose Player who bets. SB calls. BB calls. I make a crying call w my overpair.
- loose player shows 55. SB mucks, BB shows 79 (top pair, 9 kicker) but says he knows he can't beat my hand since I called, and the pot is mine.

BB is actually a reasonable hand reader (he demonstrated this in other hands from the same session). He knows he very likely has LoosePlayer beat, but he simply should have raised. From BB's point of view, my hand is very likely to be an overpair. (I think he should guess my hand to be 75% overpair, <25% 2 overcards, and tiny % chance of a full house)

The best play for BB, given he had already checked the river, is to check raise the LoosePlayer. In this case, he is risking 2BB to win a 8BB pot. Again I can't call 2 cold here, unless I had a full house (which is extremely unlikely on a 7 high board that I had raised preflop) and in which case I would reraise and BB could understand he must fold. Additionally, he is actually value betting the Loose Player. LoosePlayer does not have a 3 because he would have bet the turn, nor does he have a better 7 because he would have raised the flop. By only calling LoosePlayer's bet, it lets me call getting 9:1 odds where I am closing the action.

By the way, I think if LoosePlayer was going to make a play, he should have semibluffed the turn and bet the river. I think SB has to fold on the turn, and it is not easy for BB or I to call both the turn and the river. As long as LoosePlayer is capable of folding to a check raise from SB or BB (which LoosePlayer is not....hehe), betting the turn is the correct play for LoosePlayer.
However, I am certain LoosePlayer believes he has the best hand on the river since from his point of view, the turn and river were checked. Betting in last position on the river with a medium strength hand... donkey!!

In this hand, I think it should have helped the hand reading that it was a live game, but there is enough information available in an online setting as well.

I was very lucky to win this pot. I believe SB has A high and possibly 2 overcards, so there were ~17 outs to beat me on the river. Then I was even more lucky that BB didn't bet or raise the river. Whew, some hands you can just dodge a lot of bullets and still get paid off.

One last thing: Given the information I had in the hand, and the tendencies of my opponents, did I miss a value bet (raise) on the river? (when both SB and BB only call on the river, does this tell me I have the best hand?) I'm positive LoosePlayer pays me off, and given the situation I believe BB pays me off too.
In previous hands, BB had called preflop raises with pocket pairs bigger than 88, but then he always played it aggresively on the flop.