Optimum weight and meat quality are pretty subjective terms. They probably mean different things to me that to you.
I process both pullets and cockerels, but I do the cockerels first and usually let the pullets lay a while so I can evaluate them to see which I might want to keep. Besides, I like to only process a few at a time and keep the others fresh on the claw for a while.
My cockerels grow pretty well until maybe 20 to 22 weeks, then they really slow down putting on weight. They’ll keep growing some after that but it really slows down. So that is your target for optimum growth. I personally do not process a cockerel until it is at least 16 weeks old. Some people process them at 12 weeks but there is just not much meat there.
How you feed them makes a difference too. I don’t feed a high percent protein feed to get them to grow really fast. Mine get Grower and forage for some of their food.
Meat quality is all over the board. You can cook any chicken if you use the right method. Age has more to do with method than anything else but your personal preferences come into play a lot too. The older a chicken is, the longer, slower, and moister your cooking method needs to be.
Some people will fry or grill a 12 week old cockerel and think it is really tough to the point of being inedible. Others like how a 15 week old fries up. Pure personal preference. Your chickens are not going to be as tender as the ones you buy at the store. They are going to be several weeks older when you process them so the meat will have more flavor and have more texture. If you find the right cooking method appropriate to the age of the chicken and your tastes, even a rooster several years old can be quite tender, but it will have some texture.
Like I said, this is fairly subjective. You’ll get different answers from different people because we have different criteria.
Good luck! Hope you get something that helps out of this.