I have Blackburn panniers and regularly do my grocery shopping on my bike (kind of by necessity since the only car in our garage isn't licensed or warrented). I don't know what size your grocery bags are but I can get two or three of our groecery bags worth of shopping in each bag (although that takes some repacking of the groceries)
In terms of size, if you have the brown bags I always see on U.S. tv shows then I think you would be able to very easily get one bag in each pannier.
In terms of weight I think I have had as much as 10 kg (about 20 pounds) each side - maybe even more . Certainly I have had a six pack of beer, 2 litres of mik and 2 litres of soda, a bottle of wine, plus some other stuff in one.



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