You don't get why which turtle has which weapon, anon. It's not random, as their respecive weapons both supplement their skills and challenge their personality.
Leo is calm and calculated, he avoids taking risks. So he gets the most deadly weapon, since he won't rush to use it. But katanas also force him to be aggressive in combat to be effective and ise his skills to the fullest when he needs them.
Mikey is unfocused and easily distracted. He also has great raw talent. He gets the most difficult weapon to use, so he stays focused and has to actually train bo be effective with it and not hit himself in the head.
Raph is very aggresive and very strong. He gets a sai, a defensive blade catching weapon, which prevents him from rushing headlong into danger and/or overkill (imagine him with swords). It's short reach also keeps him close to his enemies so he can utilize his physical advantage.
Donnie is extremely smart. A trait which, while helpful in many cases, can lead him to overcomplicate things. He is also physically the weakest of brothers. So he gets a simple weapon that also helps him keep enemies at distance and multiplies the force of his swings the most.