Don't know how to do it off the size tile but you could always use a calculated filed Log(measure) and plot that instead of the measure directly
Actually, looking at this again, I'm not sure you have this option for your bubble chart (I only have this when I have a dimension in the rows/columns shelf). Jim's solution might be your best bet here.
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Sorry for all the separate posts, but I think I take that back (again). If you add the dimension to the rows/columns shelf, you can adjust the min/max sizes in the range using the method I mentioned in my first post. Then, if you remove the dimension from the rows/columns shelf, the relative sizes seem to stick.
Looks like I'm learning something new today