I built a deck with the intent of a tub last year. my tub dry is 800 LBS and with water and people I think comes out around 4500 LBs. where I would have run 2 beams normally I ran 3 and spaced my posts also closer. As an example I have 12 posts under a 12x16 deck each sitting on a precast concrete footing the tapered ones they make with a pocket for the post to land on. I also cross braced the whole side in both directions that the tub sits on. and mine only sits about 3’ on one end and 4’ on the other above the ground. I would suggest you build the deck free standing and not attach it to the house with a ledger as you can calculate the forces much easier on a free standing without trying to factor in the house design.
So far it’s made it a couple winters without trouble. There are some photos posted on page 6 of this thread.
Give us more information on the size and the tub and we should be able to give you some ideas. I built mine with an 8’ section of the rail removable and the guys that delivered the tub loved that. Also they crawl under and gave me the thumbs up and I noticed they had a bunch of blocks and stuff they might have used to brace it up if the deck was weak. The guy that sold me the tub asked a lot of questions about the deck, I gathered more than once they got one to the site and said no way.
I have also seen and I almost did this, where people sink the tub into the deck and then have it sitting on a concrete pad and the deck wraps around. If you do that the easiest way to enter and exit a tub is if it is about half way sunken or just about the height of the top step if you use steps.
Good luck we love our tub.