You'll be fine on a 650, and there's a significant weight difference with the 1000, plus most of the added weight is up high. I'd strongly recommend the 650 over the 1000 for a new-ish rider.
That said, you WILL need suspension upgrades to better match your displacement. For decades, Suzuki has sent their bikes overseas equipped with limp, lame springs barely adequate to hold the bike up, let alone cope with a large-ish Westerner. I think Suzuki offers employment as test riders to former jockeys and ballerinas or something.
Up front, I'd recommend a set of Sonic Springs in the appropriate spring rate and fresh 10W fork oil. That rate will probably be 1.1 kg/mm for you, but ask or use the calculator.
Out back, you'll need to replace the spring at minimum. One of the most cost-effective options is to send your shock to be revalved and resprung at Adventure Power Sports:
Adventure Power Sports, LLC
And of course, if you can locate a used bike with some compatible suspension upgrades already in place, that could save a LOT of cash and time. Quite a few, if not most, used V-Stroms on the market have suspension upgrades.
It's only a little awkward to ask a seller approximately how much they weigh...