Breast implants do add a bit of weight to your body.
However the breast implants only add about 2 lbs to maybe 10 lbs of weight at most to your body depending on the size of the breast implants.
The actual weight gain from breast implants depends on the size of the breast implants and the type of breast implants.
Smaller breast implants will add less weight than larger breast implants but you should not have a significant increase in your weight from the breast implants though.
Some people notice around a 1 to 3 lb increase in weight when they have breast implants of the smaller variety and other people with larger breast implants noticed around a 10 lb to 15 lb weight increase.