ever since 2007, RUSA has put an emphasis on climbing. So you will find that most brevets have a lot of climbing. If you can keep your 65 mile pace up for another 65 miles, you can finish a 200k in the time limit. I have weighed as much as 210 when randonneuring, and while I'm on the slower end of the scale, I have never really had much problem finishing. However, as a climber, I'm a good descender. I would like to get faster, so my main training plan is to lose weight. At my age, it's a lot easier than building muscle.
You don't have to do a lot of distance training to become a good distance rider. Just enough that you are used to taking long rides. If you can build up to being able to ride 60 miles in good form, you can probably go as far as your mental state will allow. So that should be your goal. Stick to 20 to 35 mile rides until that becomes a non-event. Regular (daily is good) rides of 20 miles or so will really help with weight loss as well.