Tires: rear end drift, 4wheel drive, balance weights

Question
I just purchased a set of Uniroyal Laredos for my 2003 4wheel drive avalanche. Now when I reach speeds of about 60 mph it feels as if the rear end is drifting back and forth . The drifting is really accentuated on grades of highway that have a wavy pattern. I did not have this problem before the new tires. I noticed that the drivers side rear tire has alot more balancing weight added to it than the passenger side rear tire.
Do you think that this drifting is caused by the tires?
I also had the wheels aligned when I purchased the tires.

Thanks in advance for your help.

Answer
Greg,

Did you change tire size?  Or convert from P metric to LT metric?

The balance weights would have nothing to do with a drifting.

I can not imagine what may be going except what I already mentioned - and inflation pressure - you ought to check that!