I don't really think the weight reduction of 6 rounds is really going to be noticeable. Most of the weight is in the gun itself, not the rounds. Try it for a day and see if you can really even notice a difference between a gun with 6 rounds and a gun with 12 rounds. I bet by the end of the day you will not feel any real difference.
Personally I always carry my guns fully loaded with one in the chamber. Currently I am carrying a S&W 645 that I got today and it weighs a ton but it only holds 9 rounds (8 in the mag, 1 in the pipe).
Brain (Use this one the most)