I'm overweight. Could this affect my chances of getting pregnant?

Yes. There are many studies that relate a lower pregnancy rate if one is not there ideal weight. This has to do with dysfunctional ovulation and hormonal imbalance.
Possibly. Menstrual cyclicity, and thus your ovulation, depends on maintaining percentage of body fat (not known exactly) within a range. Thus, women significantly over-or-under ideal weight may have fertility problems related to impaired ovulation. If you are irregular due to weight, it's certainly possible - otherwise, it's less likely.