Don't blindly believe everything you read on the internet, whether from me or someone else. I'm not saying that because people are purposely giving you bad information, but because we all have different conditions and circumstances. What works for me might not work for you.
When you integrate chickens you have three different things to worry about. If you have two or more fairly mature roosters, they may fight for flock dominance. Occasionally that can be a fight to the death, but usually they work out an accommodation to work together. Quite often that fighting involves a lot more chasing and running away than actual fighting, but it can be serious.
The second thing is pure integration. Chickens can be territorial. If they see new chickens in their territory, they may try to drive them away. Notice I said may, not will. Sometimes this is not an issue at all, and sometimes it is really brutal and vicious. This is where housing them near each other like you have been doing really helps. They at least recognize that the others have a right to exist there. Sometimes this part goes so smoothly you don't know what you were worried about and sometimes it is brutal.
The last one is the pecking order. This is probably where you will see some agression. This has nothing to do with size. There are plenty of times that bantams are higher in the pecking order than full sized fowl. In your case, the problem is going to be maturity. Without fail, a more mature chicken will be higher in the pecking order than a less mature chicken. I've seem 15 week old chickens establish their place in the pecking order, but that is pretty rare. Usually it takes several more weeks before they mature enough, sometimes many more weeks.
When a chicken lower in the pecking order invades the personal space of a more dominant chicken, the more dominant chicken is percfectly within her rights to peck the other chicken. If the pecked chicken runs away, all is well and good in the flock. If the chicken does not run away, it is a challenge to the pecking order status and can result in a pretty good fight. Occasionally you will get a brute and a bully that will chase the lower ranked chickens, seek them out to try to destroy them. I've never seen a dominant rooster do this. A non-dominant rooster might since he is fighting for his pecking order ranking too, but almost always this is a hen. This seek and destroy behavior does not happen all that often, but it is something you might want to watch for. I've never seen it in my flock, but others I trust to know what they are seeing have posted about it.
How can you use this information to help you with your integration. First, give them as much space as you can. They need space to run away. They need space so they can hang out in separate places to avoid that contact. The younger ones should very quickly learn to avoid the older hens as much as possible. They will be different flocks, the young ones staying as far apart as they can. You can help this avoidance by providing extra roosts and things they can hide under or behind to stay out of sight if room is an issue.
Provide different eating and drinking stations. This avoids conflict if the younger ones try to eat or drink. The older ones will use intimidation to establish and maintain their status. The young ones can wind up not eating or drinking enough.
At night, do not try to force them to sleep side by side on the roosts. This is where mine are often really brutal. It is almost always the mature hens lowest in the pecking order that are the most brutal. You will probably find that the young ones will sleep on the floor or somewhere else, maybe even in the nests. I put up additional roosts lower down but further away from the adults roosts because this occasionally becomes a problem. Sometimes it is not a problem at all.
I've had a broody wean her chicks at about 3-1/2 weeks age. Those chicks were raised with the flock and were totally integrated. To me, that is proof you don't have to wait until they are the same size as the adults to integrate. They went through the pecking order stuff, but they managed quite well.
With my brooder raised chicks, I usually let them start mixing with the adults at 8 weeks, but I give them plenty of room. My brooder is in the coop from Day 1 and it has wire sides so they can see each other. My grow-out pen is right next to the run. If I wanted to, I'm convinced I could put them together even earlier, but I have room and the set-up, so I don't worry about it. When Dad raised chicks many decades ago, he would keep them in a cardboard box on the porch for about three weeks, then take the box to the chicken coop and dump them out. They totally free ranged so space was not a problem, but he did not lose any doing that. My conditions are not the same as his, so I do things a little differently. Your conditions are almost certainly different than mine so you may need to alter things some. Hopefully with this very long post, you can come uo with a way that will work for you.
Good luck!!!