I've never needed to lose much weight, but when I needed to lose about 15 lbs. and took a 1200 mile tour down the west coast to help do so, I was chagrined to find I had gained 2 lbs. after 4 weeks of riding. But man, were my legs in shape!
From all I've heard and read a slow, gradual weight loss is the healthiest and most likely to "stick".
14 weeks is enough time to get in shape for a century, especially if you've already been riding some. Ride at least 3 or 4 times a week, maybe 30 miles each time with occasional longer rides. Gradually make your longer rides up to 50 or 60 or even 70 miles. Then don't ride the three days before the century. You'll be fresh and ready. If you're like me it will still be a significant challenge. I've never ridden a century that was "easy". The best I ever did was when I felt really good until about mile 80. Then those last 20 were typical drag-my-butt-home miles.
Don't be too proud to abort the ride if you must - don't beat yourself up too badly. But I'd recommend not quitting at the first inclination. On my last century I was worried about my conditioning. At about 55 miles there was a headwind and I was pooped. I tried to call my wife to come pick me up but there was no cell phone reception. I kept riding. The turnaround point was at 62 miles. I took a nice sandwich break and sat in a comfortable chair. (Still no cell phone reception.) When I got back on the bike the wind was now at my back and the rest rejuvenated me! From mile 62 to about mile 80 I actually enjoyed myself! The last 20 was drag-my-butt-home time, but I knew by then I would make it. And I did. I was very glad I hadn't been able to call my wife.