What is the body language when the smaller cat attacks? Ears back? Is he growling? Is his back ridged? Does he go for the big guy's neck? This is aggressive.
Or does he crouch - his tail "flat" and maybe twitching slowly - then does he wiggle his butt and bolt at the older cat? And then does he just pounce on him? This is play.
When he pounces - if he pounces - is his tail up? This is DEFINITELY play.
Is his tail flat - and his ears are back? This is aggression.
Either way, with two new kitties, even though you've had them several weeks, I'd start over and treat it like a new introduction. The only question is - which kitty gets confined and which kitty gets the rest of the house? I don't know the answer to that question. If it were us, we'd probably put the one that is clearly going to be the alpha in a separate room, and let the scaredy cat have the run of the house.
He needs time to establish his territory as he's not getting the chance to do that.
In the meantime, purchase some Feliway spray - or the plug-ins. I'd also consider purchasing some Calming Flower Essences for your other boy. They work well with some cats, and others don't respond - it's a kind of "nothing to lose" thing if you can afford to spend the money. It all can be purchased here: http://www.catfaeries.com
If you go for the spray vs. several plug-ins for rooms, spray it liberally pretty much everywhere except near the litter boxes. Re-spray every three days or so, and keep it up for like a month.
OK. Are you willing to replace the door of a room with a screen door temporarily? This is really the best way to do it.
Put aggressive kitty in the separation room with litter, food, water, toys, etc. To help prevent him from getting bored, make sure you spend time in there with him, even if you're not playing with him. Just reading, watching TV, ironing, whatever. Also, consider purchasing bird feeders to put outside the window. Even the ones with suction cups are great. It's Cat TV.
With aggressive kitty, at a regular time every morning and evening, give him a minimum of 10 minutes of interactive play with a wand toy or laser toy. Get him moving and running - use up some of that energy. Praise him to high heaven for playing with toys.
Let the other kitty get comfortable in the house. Make sure he gets lots of attention and play time too.
Next, take hand towels or rags or something (preferably washed without strong scented dryer sheets) and rub big kitty all over with a couple of them. Put them under aggressive kitty's food dish, and after your play sessions, leave treats out for him on one with big kitty's scent on it. Do the same thing for big kitty with aggressive kitty's scent.
This will help the cats come to associate each other with "good" things.
It will also help them associate treats with proper play - and the scent of the other cat with proper play and treats.
Since they're not kittens, they probably respond to catnip. Cats become insensitive to catnip if overexposed, so never leave catnip toys out for more than a day or two at most, and then pick them up for a week or two before putting them out again. BUT if they do react to catnip toys, give each kitty a catnip toy. Let them rub and drool all over it. Make sure you keep track of which cat drooled on which toy. Pick them up, and put them away for a week. After a week, give the toy to the opposite cat.
Any time you see them sniffing at each other through the screen door and they're not growling or hissing, or aggressive kitty isn't lunging at the screen, praise them both to high heaven.
After a couple of days, if there's no signs of aggression (or fear) through the door, then let big kitty into aggressive kitty's room for a supervised visit that should last no more than 15 - 20 minutes.
Keep an empty can with coins in it handy - or an air can. If aggressive kitty goes after big kitty, shake the can of coins loudly, or blow the air can - point it up towards the ceiling so there's no danger of "hitting" a cat with the air (it can freeze the skin). The noise of the air can hissing or the loud noise of the coins will startle him out of the attack. NEVER physically intervene when one cat is going after another. Ever.
I would think two weeks of this should do it - lengthen the time of the visits if things are going well.
The important thing is to get the kitties to associate each other with good things, to learn what appropriate play is - and he's got to have an alternative for that energy, so keep up the interactive play times with him. The Feliway and Calming flower essences should help the atmosphere.
...and big kitty gets time to make the home his territory, and aggressive kitty gets time to calm down and to learn how to redirect that energy he's got onto things other than the other cat.
Now..... all of that said and done.... if it is all just play, then I'd still do the Feliway, the Calming flower essences, and the scent swapping. I'd still recommend putting up bird feeders - which can literally absorb hours of time - squirrels and birds that figure out the cats can't get them often taunt the kitties and it's a blast. I wouldn't separate them, but I would give aggressive kitty alone play time (take him into a room and shut the door) twice a day for a minimum of 10 minutes - again, with the treats put down afterwards on the towel that smells like the other cat.
I'd give the big guy some time to let the aggressive one know he doesn't want to play - but if he's being totally cowed, use the air can or the can of coins to get him to leave the big guy alone. But when he IS playing appropriately - with you interactively with a wand toy, or with other cat toys - praise him to high heaven. He needs to understand what you do want as much as what you don't want.
I really hope this helps,