if the string stretched it would have increased the bows weigh
Not noticably by any measurement I've ever taken. It will increase drawlength and therefore will store more energy, but draw weight is most affected by pre-stress on the limbs, which is controlled by the cable length. When a bow company designs a cam with a range of drawlengths, the poundage doesn't change appreciably by going to a longer one. However, shorten the cable by even 1/2" and you'll see a big difference.