I weigh mainly for peace of mind but it does make a very small but noticeable difference in grouping at longer range (45yds+), not so much in size of group but more circular groups with fewer pellets breaking out from the main cluster. Over the chrono weighing takes my current batch of pellets from 10-15fps variation down to 2-5fps difference, again it may not make much difference but in my head its a definite confidence boost.
I used to size but after a fair bit of testing came to the conclusion, for that particular gun, it didn't warrant the effort for no appreciable difference. I know other who swear by it so I guess its a what works for your particular gun/barrel/pellet combination.
For me lubing has generally made groupings no better or worse, I've yet to get a gun to shoot better with lubing but again its what suits your particular gun/barrel/pellet combo.
Other than trying it for your yourself there's no hard and fast rules it seems
one of the joys of airgunning