[RobNottsUk]

So you're first to act and check, your opponents know you are likely to have the nut Lo because you're very tight. So now dude with a Lo, nevermind the nut Lo, knows that if he bets, the Hi will raise, and you will fold even the nut Lo and that player gets money back plus 1/2 of what you leave behind. Sounds great deal!

If there's 100 in pot, it goes check, check, bet pot. You're asked to call 100 to win +50, or if nut Lo overcalls 100 for 1/4 of 400 which is 0. Folding in that situation fearing overcall guarantees a loss.

With check, bet 1/2 pot, raise pot, goes :

100 -> 150 (50 bet)
150 -> 400 (50 call, 200 raise)

Now you have call 250, to win 1/4 800, which is EV of -50 when NLo is in middle, but could be -ve if NHi was first bettor and re-raises again.

With check, bet pot, raise pot, goes :

100 -> 200 (100 bet)
200 -> 600 (100 call, 300 raise)

Now you have call 400, to win 1/4 1200, which is EV of -100 when NLo is in middle, but could be -ve if NHi was first bettor and re-raises again.

Has a stop bet with Nut Lo out of position got value? By betting less than the pot, you encourage a call rather than a bet by Nut Lo (or a fold if they're concerned about being quartered), and an easy call of pot raise by Hi back. You may pick up 'loose' calls by 2nd Nut Lo's who suspect you have nut Hi, and you put the Nut Lo in the middle, in the same situation, as the one you faced, when check-ing, having to call and fearing getting quartered with a possibility of yet another raise.