The same logic that works against the West has also been working against Putin: "what are you going to do about it; escalate into WW3?"
And then NATO would have to respond when cruise missiles started flying into some of their member states.
The US finally said no to the specific plan, and put forth the general rationale for the more general no when it did so.
(OTOH, the tolerance for acts that might be seen as provocation by Russia among NATO countries—at least those on the Eastern flank—is going up rapidly, with Estonia and Lithuania calling for a NATO-enforces No Fly Zone, and Poland hold-my-beering them and calling for a NATO peacekeeping force in Ukraine.)
/1 Of the declared $800mil Anti armor launchers account for ~$400mil, then the other $400mil pays for some small arms, personal armor, ammo and 100 drones? Its pure mil complex walfare program.
It's not so much that putin doesn't have the balls to escalate into WW3, it's that supplying weapons isn't considered very escalatory (for all sides involved), so putin is more likely to let it slide rather than escalate himself. It's not something that can universally extended (eg. to no fly zone or boots on the ground).
It wasn't seen as too likely to effect the conflict, but as the conflict drags out it becomes a greater irritant. Russia is recently openly threatening to attack “supply lines” of those arms if they continue; since anything in Ukraine is already clearly subject to attack this at least implicitly is a threat to potentially attack convoys and logistics points outside of Ukraine.