Gawd, who can lose weight riding base? Not me, that's for sure.
The old school formula for serious racers was 1000 miles of base (about 1 month), which begins following 2 or 3 months virtually off the bike. People don't take months off the bike any more. It's probably almost as important to spend time in base to minimize risk of burn-out, like, mid-summer. But, IMO, after 6 weeks, you're probably going to plateau and not gain much from additional base work.
I'll probably get slammed for this (what the hey, bring it on. Discussion is good), but it may be a better time of year to work on strength, and do the endurance work later*, when days are longer and temps warmer. It's awfully hard to work on endurance this time of year, unless you live in the deep south or don't have a daytime job.
*Both strength and endurance work will slow down your racing speed. But, if you're going to be doing any srength work with weights, lifting heavy, you definitely want to have that phase well behind you before trying to be competitive. You need time to translate gym strength to bike strength, and re-develop speed. Endurance work will just slow you down 'til you recover. And all this assumes you're in pretty good shape to begin with.