The longer the bullet, the faster the twist required to stabilize it - it's really not related to bullet weight, except that given a fixed bore, the length of the bullet will increase when the weight does, for the same material.
55gr FMJ lead core bullets need at least 1x12 to stabilize over a wide temperature range. Early 1x14 and 1x16 .223 barrels worked all right most of the time, but failed to stabilize bullets in the heavier, denser cold air of winter or arctic conditions.
A faster twist will stabilize shorter bullets, as well, but in the case of some lightly constructed varmint bullets, a 1x7 twist, coupled with high velocity and thin jacket can result in the bullets disintegrating after leaving the muzzle.
The 1x9 twist is ideal for current-issue lead and steel-core 62grain M855/SS109 ammunition. It also does just fine on 55gr FMJ ammo, up through maybe 70-75 grain lead core bullets.
The military adopted the 1x7 twist as a compromise in order to stabilize the very long L110 (M856) tracer round, which would really prefer about a 1x5 twist, and the 1x9 which would be ideal for SS109 (M855) ball ammo.