I've used all different weights over the years but predominantly very light e.g. 2lb 5oz harrows. This season I scored a ton in first game using a 2lb 11.6. However not only was the bat weight vastly different but so was my technique. The handle then broke and this put the weight up again. I've actually added a second grip so we are looking at 2lb 14 or there abouts now. I usually open but dropped down to 5 on Sat and was involved in a run chase with spinners at each end, no cuts or pulls. Will be much more interesting when I use it to open against the new ball. I find more important than weight or pick up is feel in the hand. Rather than hundreds of bats I seem to have hundreds of grips. So for me handle size, shape and grip seem to play a big part in my mind.
The game I had to use my lighter bat while my new one was broke I scored 1. That was prob more down to a good bowler bowling a good ball as opposed to the bat though.
However finally there is no doubt that the difference in weight between say 2lb 5 oz and 2 lb 14 oz is noticeable and your technique and range of shorts will be different. In my opinion I can't see 2ozs up or down is one noticeable or two going to affect your batting in any way except possibly in your head!