Please tell me the appropriate weight gain per week for a Bernese Mountain Dog puppu

There is an excellent BMD guide, including expectations for puppies at this link:

http://www.bmdcsew.org/pbg/pbg.pdf

-Beth

Worry less about how much it is gaining, and more about whether it is at or approaching the ideal body gain. Butterballs are cute, but waists are healthier, see http://www.puppychow.com/products/popup_body_condition.aspx

It can depend greatly depending on each individual animal. Just like children the norms aren't always followed.
I would ask the breeder what to expect as they are the best source for your specific dog. If the breeder was a reputable one they should give you all the info you need.