Detail about weight lifting but not the riding?
I think you might want to stop the weights if you feel it takes anything away from bike training.
Training for a hard double century is not that different than training for any hard ride where you are concerned about performing well.
Do your intervals, but also get some long easy rides in. Recover sufficiently before the big day.
read this:
JV's Cycling Blog: Training for Ultra-Cycling Events
I recommend relatively short and hard interval sessions 2 or possibly 3 times, with one longer ride at a fairly easy pace too, each week. Active rest, or actual complete rest 3 or 4 days per week. This is a high intensity- high rest approach. Interval rides might only be an hour long. Zone 4 and 5 intervals. The long ride might be 3 hours or so. Zone 2, maybe a little zone 3 sprinkled in.
If you don't like doing interval type work, then a couple moderate length tempo/zone 3-4 (sweet spot) rides might substitute, but they can sometimes lead to burnout. 90 or 120 minutes of that stuff is hard.
Bottom line: you need to stomp on the gas at least a little bit to evoke adaptations.