In the worst case, you would react by directly attacking the adversary that launched them. Hopefully by the time things had reached that level you would have had an opportunity to exhaust all diplomatic channels and could have found a more peaceful resolution.

With technical escalation.

https://en.m.wikipedia.org/wiki/Barrage_balloon

Perhaps not so well when everyone's a Captain Kirk.

Investment would lean back towards gun based AA, like anti-air artillery since the objects are so high. Investments are already going back into that direction as cheap drones like the SHAHED are easily managed affordably by systems like Gepard. It's actually quite fun to see these systems revived.

I think laser-based weapons would be more likely, honestly. It should be possible to heat up a balloon enough to melt the envelope without an absurd power supply.