I can't tell you exactly what to do with your set-up, but maybe I can tell you a bit about their behavior. You have two different kinds of aggression to worry about,
One type of aggression is pure integration. This is where a flock does not recognize the others as part of the flock. They tend to guard their territory from intruders. Not always, and usually it is a hen but it can be a rooster, but sometimes they will attack and try to kill the others if they won't leave the territory. That's where housing them side by side for a while comes in. They see each other enough to recognize the others as part of the flock. At the age of your chicks, that is probably not an issue from their side. They are not mature enough to try to defend their territory. The older pullets' behavior could be affected by this some, though.
The other issue, and your main problem, is the pecking order. Like other social animals such as a pack of wolves or a herd of cattle, each chicken has its own social place in the group. That allows them to live and work together peacefully. But that social position is determined by fighting and intimidation. Size really has little to do with it. It is more the spirit in the chicken. You will often see bantams ranked higher than full sized fowl in a mature flock.
More mature chickens automatically rank higher than less mature chickens. If a chicken lower in the pecking order invades the personal space of a higher ranking member of the flock, that higher ranked chicken is perfectly within their rights to enforce their pecking order rights, which they usually do by pecking. As long as the weaker runs away, everything is back to normal in the flock. Intimidation worked. But if the younger does not run run away, it is a challenge for a better position and a fight can break out. The higher one does not always peck when their personal space is invaded, but they have the right to peck if they feel like enforcing their rights. And sometimes they keep the lower ones away from the food and water as part of that intimidation.
My most recent broody raised her chicks with the flock. She took care of the integration issues. But she weaned them at 3-1/2 weeks so they had to make it on their own with the flock. Those chicks, while fully integrated, are still at the bottom of the pecking order. If they invade the space of older chickens, they get pecked. So the chicks spend their days as far away from the older chickens as they can. As long as they can stay away, life is pretty peaceful, but if they are forced to stay in the same area as the older chickens, it can get ugly. This happens with mine on the roosts at night as they are settling in to sleep. Certain older birds will actively position themselves to peck the younger birds. In my flock it is almost always a lower ranking member that does this, not the dominant rooster or the more dominant hens. I set up a roost lower down and separated from the roosts to give those chicks a place to sleep. I have had it so bad that the chicks started sleeping outside the coop to get away from the bullies.
I don't know what your set-up is like, but some of the things that can help if you can manage them. Set up separate feeding and watering stations, in the run and in the coop. The older ones will have more trouble guarding both, plus it allows the younger ones to eat and drink without challenging the older ones.
Give them as much space as you can. I free range mine so they really don't have conflicts during the day. You may not have that possibility.
Give the younger ones ways to hide and get away from the older ones. Try not to set it up where they will not become trapped and can't escape of an older one corners them, but give them things to hide under or behind. Maybe a piece of plywood or something a foot or so wide and about 6" above the floor of the coop or run. Or something in there vertical where they can stay out of sight.
You can expect the pecking order stuff to continue until the younger ones are mature enough to establish their position in the flock. That could be when they are as young as 14 or 15 weeks, but more likely a month or two later.
Additional perches and roosts come in real handy, during the day as well as at night. Your younger ones may not be roosting at night yet but they can use perches.
Good luck! It is not always easy and there is some danger for the younger chicks but it is not always a disaster either.
