It is best to wait a longer. It does take babies about 6 to 8 weeks before they sleep through the night and some a little longer. At 2 1/2 weeks babies usually just wake up to eat and go right back to sleep anyway. Besides, feeding the baby too early like that can also lead to early obesity in the infant which isn't good for it either. I have 4 grown children and a grandbaby that is 8 days old. I remember how tired I was getting up with my own and I am sure they are just exhausted, but from experience I would suggest waiting a bit.
Grandma, you can only suggest what you think is best. Remember it is your son's turn to make his share of parenting mistakes. Hopefully none of them will be detrimental to the babies health. Try not to worry.