I moved from a 2.8-2.9 to a 2.13 for Winter nets, and found that I didn't have to try overhit the ball. Helped a lot with my technique, and I have since then moved down to a 2.9-2.11 weight range. I think it's all down to preference. Big hitters don't all use heavy bats, I think Warner uses a 2.9, and Mal Loye used a 2.6, which he used to hit big slog sweep sixes off the likes of Brett Lee. It's entirely down the batsman's technique and preferences, no, the technique doesn't change the laws of physics, but the batsman themselves should dictate the ideal weight of bat they use.
Going heavier then down a bit worked for me, but won't work for everyone. If you can't get the ball off the square, I'd suggest getting some throwdowns, not trying to hit too hard, getting your timing right and making sure that the bat isn't a plank BEFORE deciding to change weights. It should become a bit more obvious what's not working for you after hitting a few buckets.
Pros and cons of heavy bats:
Generally more forgiving, which adds a little extra punch to the shot
Will generally last a bit longer
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Will wear you down quicker
Lower batspeed for those last second adjustments
Harder to sell on
Pros and cons of lighter bats:
Quicker batspeed, allowing for good adjustment and easier mobility for deft late cuts and flicks
Less wearing out of the arms, which will allow for sustained use over a long innings
Easier to sell on
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Generally more prone to breakages
Generally not quite as forgiving as heavier bats, so can lack that extra punch a heavier bat can offer.
I've probably missed out something obvious, but as you can see, there's not really anything in particular to stands out in favour of a heavier or a lighter bat. I could never have as much success as someone like Smiley or Manoramic on here with the 3lb bats they use, nor could I use a 2.6 bat as effectively as some folk on here do.
If it feels good in the hands, isn't too heavy or too light and taps up well, as a general rule of thumb, it should be fine for you to use.