Not if you have the ability to play after the flop and fold the hand even on a favorable flop if you feel you are beat. Lets say you raise to 250 (5x). Is the extra 100 really going to make the BB fold a hand here that he called 100 more with? Are you really gaining any extra information from raising more? And if the BB does call, are MP1's odds really so much worse now that he will fold a hand that he would have called with when its only 100 more to him?
Instead you've built a bigger pot, preflop, with a hand that is very vulnerable on most flops and gained little or no extra information by doing so.
The difference between 150 and 250 is huge at 25/50.
Say we raise to 150, it folds to BB - now he has to assume that the limper will call this small raise behind him and will
definitely call it if he himself calls, so we can consider that 100 that limper will call to be already in the pot. So the pot is 75 (blinds) +50 + 150 +100 = 375 and it is 100 for BB to call, so he's getting 3.75 to 1.
Now say we raise to 250, it folds to the BB. Now he can't be sure that the limper will call this large raise, and when he looks at his pot odds he can see that there is 75+50+250=375, but now he has to call 200 so he is getting a little less than 2-1.
Now, BB is playing this hand OOP against 1 or 2 players, but in the first example he is getting such favorable odds that he may feel inclined to call with his small PP for set value, suited aces, etc. In the second example he is not getting particularly attractive odds to try to play a pot OOP against somebody who has this time declared that they have a big hand.
In regards to your last point - we're not trying to gain information here, we're trying to get value from our jacks.