This isn't really a clear cut area, as much of the data evaluating effects of contraceptive preparations don't bother to evaluate whether the progestin or estrogen may be contributing more or less.
From everything I've seen, the gain in fat mass which can potentially occur in women on birth control is associated more so with the progesterone or derivatives thereof, rather than estrogens. Then again, I've even seen data which further complicates matters as the route of administration with estrogens alone, has shown very divergent effects depending upon which route you're talking about.
A more important point to make aside from that however, is that we're not talking about an absolute gain in fat mass that can't be avoided. Rather, the data is supportive of the idea that IF weight is gained, it has a high propensity to be fat mass. So, it's important that she keep caloric intake in control and keep exercising, if she isn't already.
Hope this helps.