I'm coming from a different situation but I had the same problem, heart was raring to go but legs were dead. I'm not overweight and had good lung capacity from other activities but my biking muscles weren't developed yet. After about 6 months of riding and increasing my ride lengths my legs are finally catching up. 12 weeks isn't that long, I'd say just give it time. From what I've read and heard here and other places the first year should really just be about increasing time spent riding, building a training base (what's the official term?), leaving specialty exercises for later years.