European countries sending weapons to Ukraine do not need treaties. Russia invading a European country means that Russia might invade another European country. It is just a lot cheaper to just send weapons and other support to Ukraine and have Ukraine be bombed and their soldiers dead, then to end up in a direct war with Russia.
For the US Ukraine is a problem, as being soft on Russia, means other countries who want more land could attack countries, which the US has intressts in. For example China might see the US Ukraine support and figure invading Taiwan, just means they need to pay a lot of money to US lobbiest to avoid a US response. That might be wrong, but certainly not a good look.
As a bit of context. Abkhazia is internationally recognized as part of Georgia, but since 1993 declared indpendent with strong Russian ties and not under control of the Tiblisi government. There have been multpile wars with Georgia involving Abkhazian troops with Russian support.