This is what I was thinking. you could sister the deck joists around your new post. depending on your access to the underside, you would only have to cut out like one piece of deck, trim it down and replace. could use threaded rods with bolts and washers on either side. no foundation work necessary. i'm sure the foundations you have are fine for the additional weight.We do get crazy winds here - do you really think the weight of the arbor wouldn’t be enough to offset the winds? I hadn’t thought about that angle. Is there a thought of XX pounds will resist X mph winds?
I’m thinking I’ll have 6X6 posts with several 2x10/12 and such up top for weight?
Maybe it will just be easier to remove some deck boards and put the post directly into the concrete footing and reconstruct the deck around the posts..
to answer your gravity vs wind load question, the wind will push upward too, so i wouldn't count on anything to actually resist enough to not move.