I'm resembling OP's opening remarks. Age 49, 6'1" and 270 lb. (hoping to drop that down some) with 32-33" inseam, only started riding 4 years ago, and that on an old Yamaha cruiser ('94 Virago 535). I'm thinking I might "trade up" to something newer and bigger, esp. because I want to go on more and longer weekend rides.
For a while, I was thinking something like the V-Star 950 Tourer. But the more I think about it, the more I think I want something that can handle some dirt. For example, I just moved to Phoenix, and apparently there are some neat old "Wild West" ghost towns around here; but while Tombstone has paved roads going to it, some of the lesser-known ghost towns only have dirt that might not be the best surface for a cruiser.
Also, I'm hoping to do some longer crazier rides later, e.g. going back to my homeland (lived half my life in Yellowknife, Northwest Territories), and maybe driving to Inuvik on the (unpaved) Dempster Highway. (I've been to Inuvik many times, but only ever flew there, never took the road.) I can't see myself going full-dirt crazy, but more and more I think I'd really like something that won't panic when the pavement runs out.
I'm not ready to pick a specific bike just yet, but my two "data points" are that 1) I just finished reading Neil Peart's Ghost Rider
(his story of riding 55,000 miles over 14 months on his R1150GS after the death of his daughter and wife in 1997-98), so the R1200GS is definitely on my brain, and 2) I remember hearing about the Super Ténéré coming out a couple of years back and thinking "Hmmm, that looks interesting." So when the time comes, I might test drive those two to start.
My big question, though, is as a new-ish rider who's never ridden on dirt before (not even any teenage mini-bike adventures), how would the transition from "small-ish cruiser" to "1200 adventurer tourer" be likely to go? What sorts of things should I watch for? What are good ways to get some "beginner practice" on dirt/rocks/gravel? Stuff like that. I did some searching here, but didn't find any "n00b" threads (and if there are such out there, I'd love to be pointed in their direction).