I hit the ball further with a good 2.6 bat than I do with 2.12 because I can't swing it as fast. Someone already said it, people are overthinking bats and some players just hit the ball hard.
Yes you would do for example a 10 percent increase in your normal bat weight would enable the ball to be hit further but only if the bat is swung at the same speed as your 2lb 6 ounce bat and there is no loss of timing.
But if a slower swing of the heavier bat is used due to the increase in the bats weight it will not.
Therefore your 2lb 6 ounce lighter bat would hit the ball further due to your bat speed being faster.