No, once it's last counter has been removed it will be put into the graveyard as a state based action before you even have a chance to activate the hollow. But even if you activated it before you removed the counter it won't save the weaver. A creature with 0 or less toughness is put into the graveyard as a state based action, this is not destruction. Regeneration only replaces destruction.
If I have spike weaver and yavimaya hollow on the battlefield, Can I use yavimaya hollow to regenerate spike weaver after I've depleted it's last +1/+1 counter?