Weak Entities + Partial Keys + 2NF
So wouldn't a weak entity be in violation of 2nf? Because a non-prime attribute could be dependent solely on the foreign key?


No.  Consider a typical example:

SalesOrder(OrderId,OrderDate) PK (OrderID)
SalesOrderItem(OrderId,OrderItemNum,ProductId,Quantity,Price) PK (OrderId,OrderItemNum)


No OrderItem non-key attribute is functionally dependent on OrderItemNum.  OrderItemNum could be repeated for multiple orders.  In practice it's often not, but for the purposes of normalization it's just the trailing column of the primary key.