the problem is as long as the target you send up are cheaper for you to produce than the countermeasure used against them you can spam your opponent and bleed them financially while having a minimal impact on your own budget.
Air to air missiles cost on the order of $300,000.00 weather balloons cost and order of magnitude less.
If someone starts sending thousands or tens of thousands of balloons into American airspace to make the cost of shooting them down "significant", won't your congress consider that an act of war? It's quite a leap from the odd stray weather balloon to send them en masse.
We'll all have bigger problems if that day comes than the pesky billion or two it will cost from the US $773B DoD budget.
Air to air missiles cost on the order of $300,000.00 weather balloons cost and order of magnitude less.