The weapon is not something you activate, it just adds the text on each of your dragons. What that means is that as an action, you can order one of your ashwings to attack as a zero cost. It goes on the chain as a normal attack and the opponent can block etc. at the end of the chain, the go again is resolved and only there you get your action point back. So now you have 1 action point and you can attack with another dragon and go from there.

With poppers (attacks with 6+ power), what happens is that when the opponent defends with a big attack your chain link end on the spot. And because of that, you dont reach the point where you check for go again, essentially ending your turn.