What is the right amount of weight for my baby to be gaining per week?

1/2 pound per week. A half pound per week for the first two months is the usual rule of thumb; after that, a baby's birth weight should double by six months and triple by one year.
7-10 ounces. The average baby should gain about an ounce per day, or a pound every two weeks for the first 6 months or so. Over the next 6 months (or until 1 year old) babies will gain a little less than half of that. Roughly, babies should double birth weight by 4 months or so and triple birth weight by 1 year old. Some breastfeeding babies may gain more quickly, but a lot quicker and there may be issues.