[Scuba_Dave]

I would not put the hot tub on the deck
I'd cut out & build it into the deck, sticking up about 1'
I'd build something underneath to support the hot tub

What you are trying to do would probably mean a total rebuild to support the hot tub & cantilever
What you can do will be determined by local codes & your Building Dept

 

[Scuba_Dave]

How far out does the deck come from the house ?
Cantilever needs to be designed to carry the load
For a 4' cantilever you may need to go 8' in along an existing joist for support
You then need to re-inforce the exisiting deck due to up-lift from the cantilever
In some cases you need to go with a larger joist size based on the cantilever
Yours look like only 2x6's (2x8 ?)....you will need bigger joist for the cantilever
You then need a larger ledger board against the house

Local codes will dictate what you are allowed to cantilever
So the 1st step is talking to you local Building Dept on what they will allow & what they will require
You may even need to pour bigger (and more) concrete supports (sono-tubes)