While that’s a factor, it’s a very minor one - soft metals (lead and copper) are used as projectiles primarily because the bullet itself deforms to engage with the rifling when fired (softer materials also present far less wear on the rifling as a result - this is why shotguns, which are smoothbore and thus far less delicate, often use steel projectiles). The weight of the projectile is largely secondary to the mechanical properties of the material while it’s being fired.