I have a 4.49 (head size) sizer and have tried sizing, weighing, weighing and sizing.
I tried 10 pellets straight from the tin and the variation was 6fps.
10 weighed, variation was 5fps.
10 weighed and sized, variation was 4fps.
I can't say if it makes any difference to group sizes as I haven't carried out any testing.
I have found that the weight and sizes stated on the tins are seldom more than a very rough guide although the very best quality match grade wadcutters like RWS R10 and H&N Finale Match are very good weight wise.
I'm at a loss as to what the size marking actually refers to as I have tried several sizes 4.49, 4.50 and 4.52 back to front or head first into the bottom of the sizer which measures 4.49mm and they all drop in up to the skirt.
My opinion (for what it's worth) is weighing and checking for deformed skirts is worthwhile.
Sizing? Not sure, maybe with cheap pellets with poorly formed skirts it would improve performance but there are many factors to take into consideration, as we all know, what suits one barrel may not suit another.
Accurate shooting is all about eliminating the variables so it's worth a try I suppose.