I saw from the Nick series episode Lone Rat and Cubs that the Turtles got their weapons because of their actions with them:
- Leonardo was holding onto Splinter's katana as he was pushing them in a cart in the sewers, running from the Krang.
- Raphael got his sais after he fell from the cart because a sai was lodged in a wheel, and he picked it up off the ground.
- Donatello got his Bo staff because he... well, the episode didn't really say why he got his Bo, because there was one in the cart, but he didn't interact with it.
- The youngest, Michelangelo, got his nunchucks because when Splinter reached for his chucks to fight a Krang droid, it looked at the end, where Mikey was sucking on it. One of the other million things I found cute in the episode.
