Sounds like a easy fix, BUT, I was riding home and a gentleman told me it looks like my wheels are loose...so I pull over to check, nothing...but then I angled my side mirrors and can see my wheels wobbling like they are loose...took it to a shop, they checked the lugs, and they are fine....had my fiance drove on the side of me...same thing, she said the right side was worse than the left side...I just got these rooms and tires about 2-3 months ago, never had this issue before, I did have the fenders rolled in the rear and that was just last week and now this, I did ask the guy if the ri,s were put back properly and he said yes, I plan to go back and have them take them off and put back on just to see it is that, but not sure if that will fix the issue....ANY IDEAS OF WHAT ELSE MIGHT CAUSE THIS ISSUE...PICS BELOW ARE OF THE OLD SET(BLACK) AND THEN THE NEW SET(CHROME AND BLACK) OF RIMS AND TIRES...

BOLT PATTERNS FOR BOTH

5X120
18" rims all around

 

One reason could be the rims aren't centered on the hub or if you had hub centric rings they could pinched one side causing it to mount off center.

 

Could be a bent axle flange, idk how a shop could mess up centering a wheel..

You could jack the rear of the car up, block the front tires.. Then start it and put it in drive with the rear wheels removed.. I did that once and found out my axle flange was wobbly by a little bit.

I bumped into a curb a while back and that's what caused it

 

Like Burken01 said, Prop it up and check for yourself. See if it does the same with your spare tire bolted up, if so you might need a new axle shaft.

Is the issue present on the front as well?

Also I wonder if its an issue that its the BMW bolt pattern and not the GM 5x4.75" pattern.

 

Bad wheel bearings....did the 12 & 6 test and there is play and clicking, starting with that, need to be changed anyway, then going from that point.

 

Could be a bent wheel axle as well