Different molecular weights have different solubility, surface tension, viscosity, freezing point, and melting points. The higher the molecular weight the more polyether character and the solubility is due more to hydrogen bonding. If you use higher polymers, the resulting carrier effect will be better. However, I haven't seen notable difference in PEG6000 vs PEG8000 during phage precipitation, but most of the studies were done using PEG8000.
Not in my experience. I routinely buy PEG 6000 for phage precipitation, but when I have changed to PEG 8000 due to availability reasons, the result has been also very good. Phage precipiatation with PEG is very robust. When it doesnt work its normally due to a low phage production, not to a precipitation failure.