Makes no sense.
Nashville will match and then Weber is stuck there.
It makes perfect sense if the CBA negotiations go as some think they will. There is a belief that long term deals will not be a part of the new CBA, as well as with the league wanting a reduction in the percentage of revenue players get, Weber is doing this to get in under the wire in case of those changes. If the changes came through as they might, doing this makes him millions of dollars richer than if he waited till next year, under a new CBA.
This is a good financial decision. Even if Nashville matches, they are allowed to trade him later (just not the first year). So Weber could end up asking to be moved in a year or two if Nashville isn't feeling like the home it has.