you're kind of stuck!
they can try to more evenly disperse the weights, if they had them stacked, or move them if you're only hitting at a certain point.
they can use rim mounted weights IF your rims accept them (yes, it looks like $#iT, and wheeling will likely, umm, relocate them)
you can try to have the tire balance with inside patches, which is a real pain for the tire guy's to have to mount and/dismount. you might even have them balance the rim first with tape weights on the inside, which may lessen the amount you need with the tire mounted.
or, you can run either the beads or equal, both of which are poured into the tire, and balance things out as you drive each time (don't ask me how it works
, it just does)