Eating too much will lead to weight gain, not large breast implants.

It sounds like you have stumbled into a Urban Legend. There is nothing about biologically non active breast implants which would cause you to gain weight. There certainly are many ill effects you might experience from overly large breast implants. These include ripples, palpability, pseudoptosis, drooping, and even breakdown of the breast tissue and skin with exposure of the implant. Only consuming more calories than you burn will make you gain weight. I would encourage you to think twice before getting extremely large breast implants for the above reasons.