Briefly, the weight of the bullet is not the real factor that determines the appropriate twist rate. It is the length of the bullet. The reason that bullet weight is used so often in reference to twist rate is that, generally, when a bullet is made heavier, it must be made longer. Since the diamter of the bullet cannot be altered, the only way to add weight is to make the bullet longer. The longer the bullet is, the faster the twist rate needs to be in order to stabilize it during flight.
Some bullets of the same caliber can actually be lighter, but longer. This is due to the materials used to construct the bullet. For example, a 30 caliber bullet of 165 grains, can be shorter than a bullet of 163 grains weight if the 163 grain bullet is armor piercing. Since steel or tungsten have a lower weight per unit than lead, the same weight of steel will take up more space than the same weight in lead.This makes the bullet longer, but of less weight than a traditional lead bullet of the same weight.
Thw 1:7 twist rate of your barrel means that for every 7 inches that the bullet travels down range, it will rotate 1 time. Generally, for that rate of twist in a 22 cal barrel, the 69gr through 80 gr lead/copper bullets will provide the best performance.