In the op, you stated you had 4 hens and a rooster that are 2 years old, this spring you increased your flock by 4 times that number. At this time, things are approaching full size and it sounds like tensions are rising in the flock.
There is kind of a pet theory that if animals are raised together, they will get along, but this is not true of chickens, and very often, as chickens grow up and take up more space, you get this rising in tension.
What does your run and coop look like, it sounds like you should have enough room. But regardless what we think and measure, your flock may be feeling too tight. And this is summer, in the dark days of winter, this will become much worse, as they are confined to the roost nearly 14 hours a day.
I think either the rooster needs to go, or some of the chicks? Try pulling some and check the tension in the flock, always solve for peace of the flock. It is no fun to have an upset flock, and fighting are always upsetting for all the birds, even the ones not in the chase.
Mrs K