River Raise Sizing

I ran into 2 similar spots in a recent session that have me wondering about my approach to river raises with strong hands. In both cases, against different opponents, I river the nuts and get led into with a PSB. Now this is where my reasoning and assumptions may start to falter. Smart poker players will often make big river bets, near pot-sized, with strong made hands, knowing that it is often perceived as bluffy ("Why bet so much with a monster? Don't you want to bet an amount that will get called?"). Well, there's that little bit of reverse psychology, but there's also the important details of that hand in question - What has my opponent done to reveal the relative strength of their hand, and based on that probable strength, how big of a bet can I get them to call?

If I know my opponent likes to make a PSB with a strong hand, then I should be inclined to make a hefty raise, knowing that it will be hard for my opponent to fold.

Full Tilt Poker, $0.25/$0.50 NL Hold'em Cash Game, 6 Players
LeggoPoker.com - Hand History Converter
CO: $50.75
BTN: $91.40
SB: $82.55
Hero (BB): $52.20
UTG: $50
MP: $23.45
Pre-Flop: 8 7 dealt to Hero (BB)
4 folds, SB raises to $1, Hero calls $0.50

Flop: ($2) T 2 J (2 Players)
SB checks, Hero checks

Turn: ($2) 6 (2 Players)
SB bets $0.50, Hero raises to $2, SB calls $1.50

River: ($6) 9 (2 Players)
SB bets $5, Hero raises to $21,
...
...
So not only do I river a flush, but I river the immortal straight flush, which is extra lovely given that it so well disguised and likely to get action from big flushes. So I make a full pot raise and...
...
...
...
SB folds

Results: $16 Pot ($0.80 Rake)
Hero mucked 8 7 and WON $15.20 (+$7.20 NET)

I think I miss a couple of clues here. One is the PF min-raise, a likely sign that I'm not up against the sharpest of poker players. Not only does this make it more likely that he would call a smaller raise (say to $12-$14), but also that he might come over the top with any type of flush.

The second time around, against a different opponent, the line and situation are quite different...

Full Tilt Poker, $0.10/$0.25 NL Hold'em Cash Game, 6 Players
LeggoPoker.com - Hand History Converter
UTG: $30.66
Hero (MP): $32.99
CO: $25.57
BTN: $31.53
SB: $25.10
BB: $25.76
Pre-Flop: 8 7 dealt to Hero (MP)
UTG folds, Hero raises to $0.85, 3 folds, BB calls $0.60

Flop: ($1.80) 6 2 5 (2 Players)
BB checks, Hero bets $1.20, BB calls $1.20

Turn: ($4.20) K (2 Players)
BB checks, Hero checks

I could certainly 2-barrel here and likely take the pot down, but I'm willing to take a free card, and figure to get more action (if I hit) after taking a bet-check-bet line.

River: ($4.20) 9 (2 Players)
BB bets $4.20, Hero raises to $16,
...
...
Bingo once for the 9, and twice for the pot-sized lead. Now, given the line here, my opponent's range is pretty wide. There aren't a lot of monster hands out there, so the hands that I should be targeting for value are hands like K-x, and medium and small pocket pairs like 77/88/TT/JJ. Sets are much less likely given the action. So, a medium-sized raise is probably in order, somewhere along the lines of 2.5x-3x. Instead, I make it 4x....
...
...
...
BB folds

Results: $12.60 Pot ($0.63 Rake)
Hero mucked 8 7 and WON $11.97 (+$5.72 NET)

Any insights out there on how to approach these spots, or river raising in general?

Hindsight's 20/20, so we'll check in the next time I make a sad, small raise, and get called by the 2nd nuts. At least, the next time around, I hope to have fully considered my opponent and the situation.