How do I make sure the deck can handle a heavy spa?

Your instinct about the weight is right, and honestly you might be underestimating it. Water alone runs about 8.3 pounds per gallon, so a tub that size can hold 350 to 400 gallons. Add the shell, the cabinet, the equipment, and a few people in there, and you can easily crack 5,000 pounds. Spread over roughly 48 square feet of footprint, that's working out to over 100 pounds per square foot in the tub zone, when a normal deck is designed around 40. So no, thicker lumber alone doesn't get you there. The fix is structural, not just upsizing. What actually works is treating the area under the tub like its own little structure. Run a beam directly under the tub footprint, not just near it, with its own posts down to footings. Don't hang the tub zone off the rim joist or rely on the main deck beams a few feet away. Joists under the tub should be doubled or spaced at 12 inches on center, and I'd use 2x10 or 2x12 depending on your span. The posts under that beam carry a serious point load, so your footings need to be sized for that, not just for general deck duty.

Since you allready have footings poured, check where they are against where the tub support posts need to land. If they don't line up, that's a problem to solve now, not after cutting lumber. Also think about access. If the tub ever needs service underneath, you'll want a way in without crawling thru the framing you just built.

One more thing worth saying. A spa load like this is exactly the situation where having an engineer or a designer look at your drawings for an hour or two is money well spent. They can size the beam and confirm your footing capacity against your soil. It's a lot cheaper than finding out the deck is sagging six months after the tub is full.

I did almost this exact build two summers back and the thing that saved me was dropping a beam under the tub zone instead of trying to make the main deck framing carry it. I also kept the tub corner independent of the ledger side, so if anything ever moves it's not pulling on the house connection. One thing I'd add: leave yourself a hatch or removable section of decking over the equipment pack. I skipped that and regretted it the first time the pump needed attention. Also fill the tub in stages the first time and watch for any bounce before you commit to the full load.

One thing I'd check is what's under those footings. Mine sat fine for the deck itself but when I loaded a spa on top, one corner sank maybe half an inch because the ground there was soft from a downspout dumping water right beside it. Moved the downspout, but the lesson stuck. Also grab the tub manufacturer's spec sheet before you finalize anything. They usually list the filled weight right on it, and some even tell you what kind of base they want. Makes the engineer conversation way easier when you've got real numbers instead of guesses.

Update: went back to my plans after reading these and the seperate beam idea makes alot of sense. Also checked my yard and guess what, there's a downspout dumping right where two of my footings sit, same problem the third poster ran into. Rerouting that before I build. Also finally pulled the actual spec sheet for the tub I want and the filled weight is higher than my estimate, so glad I didn't start cutting yet.