Min raising?

I don't understand it. Genuinely. I see people min raising with top pair J, which to me is thick, because it's a hand which is easily outdrawn on later streets. You want to be getting maximum value out of it and so wouldn't you just raise 3x or more, and if you take it down you'd be happy anyway?

If you have the nuts and you min raise, to me it sets off alarm bells and I'll be more likely to fold a reasonable hand Heads Up. Raising 3x to me doesnt really make a difference, people who think they have a good hand will call anyway, so why lose value? I think the only time I might min raise would be flopping the stone cold nuts in a pot with 4 or more people, so if one bloke calls, the rest are getting odds to do so aswell, building the pot to then betting the turn hard. Meh, thats just me. Any comments on how I'm wrong would be appreciated

Just on 10/25 at the mo, up a buyin after fishing hard for a flush after I flopped mid pair and a draw...fuck it i'll just post it up.

PokerStars Game #18105894394: Hold'em No Limit ($0.10/$0.25) - 2008/06/13 - 08:20:31 (ET)Table 'Pemba II' 9-max Seat #2 is the button

Seat 2: TonyP22 ($23.95 in chips)
Seat 3: Hayate1337 ($15.90 in chips)
Seat 4: Tuwei168 ($25 in chips)
Seat 6: tiburoni ($5.10 in chips)
Seat 7: francisbbg ($11.90 in chips)
Seat 8: k030101 ($24.25 in chips)
Seat 9: Chris994 ($24.30 in chips)
Hayate1337: posts small blind $0.10
Tuwei168: posts big blind $0.25
KillingAce: sits out
rockandrock: sits out
*** HOLE CARDS ***
Dealt to TonyP22 [9h 6h]
tiburoni: folds
francisbbg: calls $0.25
k030101: folds
Chris994: calls $0.25
TonyP22: calls $0.25
Hayate1337: raises $0.50 to $0.75
Tuwei168: folds
francisbbg: calls $0.50
Chris994: calls $0.50
TonyP22: calls $0.50
*** FLOP *** [9d 7h Kh]
Hayate1337: bets $1.25
francisbbg: calls $1.25
Chris994: folds
TonyP22: calls $1.25
*** TURN *** [9d 7h Kh] [3d]
Hayate1337: bets $3
francisbbg: raises $3 to $6
TonyP22: calls $6
Hayate1337: raises $7.90 to $13.90 and is all-in
francisbbg: calls $3.90 and is all-in
TonyP22: calls $7.90
*** RIVER *** [9d 7h Kh 3d] [2h]
*** SHOW DOWN ***
Hayate1337: shows [Jc Kc] (a pair of Kings)
TonyP22: shows [9h 6h] (a flush, King high)
TonyP22 collected $7.60 from side pot
francisbbg: mucks hand
TonyP22 collected $34.90 from main pot
*** SUMMARY ***Total pot $44.70 Main pot $34.90. Side pot $7.60. Rake $2.20
Board [9d 7h Kh 3d 2h]
Seat 2: TonyP22 (button) showed [9h 6h] and won ($42.50) with a flush, King high
Seat 3: Hayate1337 (small blind) showed [Jc Kc] and lost with a pair of Kings
Seat 4: Tuwei168 (big blind) folded before Flop
Seat 6: tiburoni folded before Flop (didn't bet)
Seat 7: francisbbg mucked [9s Ks]
Seat 8: k030101 folded before Flop (didn't bet)
Seat 9: Chris994 folded on the Flo

In hindsight I think I probably should have pushed the turn (even folded???) but hell, I'm still learning.