If a die is weighted, the first roll is no longer 1/6 probability to get a 7

Yes, actually, it is. No matter what the first die lands on, there is a 1 in 6 chance that the second die will land on the corresponding value necessary for a “7”. You could glue the first die to the table with “6” (or any other number) showing, and there will be a 1 in 6 chance that the second die will bring the sum to 7.