what did you do to cause it?

where do you live?

do you park outside?

what year is it?

how many miles?

what mod's?

Little rubber dealy-bopper(s) failed. Dirt common, the little rib that holds the pieces together tears and the hub wobbles. Easy fix, drop the wheel, add some rtv where the blocks have gotten a bit worn or sloppy, reassemble and forget about the issue.

When you say it can be wobbled.....How much?  There is always some play in them to rotate back and forth a little bit (rotate).....the pulley should not move in and out much if you grab it top/bottom and wiggle it (wobble).

Just took a look in the Clymer.  It didn't mention anything about wobble limits or loose movement limits.  

It says you should inspect the rubbers for a tight fit.  If they are loose, replace.  The metal dividers in the wheel should be checked for cracks or missing pieces. Check the bearing for excessive play. (doesn't say what that is...just check for it) If the bearing doesn't turn smoothly, replace.  If the inner race has excessive axial or radial play, replace. (again, doesn't specify what excessive is)

Call a Suzuki dealer, ask for maintenance, ask them if there is a limit on the hub wabble. Kinda hint to them that you might bring it in to them if its out of limits. Ask them where they get their limits from, then go look yourself, if you can get access to where they say, if not, then go by the limit that they tell you.