The largest functioning trebuchet that I know of is the replica of the "War Wolf," built and operated by Hugh Kennedy in England. He explained that he'd found an historical claim that the WW was capable to tossing a horse into a castle court yard from 300 yards away. He reasoned that if the account were true, it should be possible to replicate the feat. He did exactly that, using an assumption that the horse would have weight some 1,500lbs. Anybody who uses Hillman and Renault cars for ammo impresses me with their design skill.
Only from video that I've seen, the arm is jointed/assembled like a split cane fly fishing rod, possibly 4-5 feet in diameter over the counter weight and likely 50+ feet in length. That means that the tower must be 30-40 feet tall or more. Yes, it is almost indescribably immense.
Be that as it may, I enjoy the entertainment of any treb with payloads of 20 lbs or less. Designed at 200:1, 4,000lbs in the counterweight is not unreasonable.
If you haven't found them so far, I suggest you look at the results from the trebuchet section of the Punkin Chunkin Contest, an annual veggie tossing event in the United States. If memory serves me, the record for the air cannon section is 4,000+ feet/1,230m, across a freeway and into the filed on the other side. They have a contest site. That implies that all the siege engines have to be trucked to the site and assembled.
You misread the question .
I have viewed much of the published material in the past , Kennedy and the Danes included , and know that on average , the larger trebuchets were about 4 stories high , 40 - 60 feet.
Given that you have told us that you have built some , I'm asking you for your opinion , base on your personal the experience, of what might be theoretically possible