The chemicals can have some bad effects unless you really know what your doing. If the chems kill off too much submerged vegetation, its possible that your pond's dissolved oxygen levels could go down and algea could start growing then the dissolved oxygen would only be near the surface of the water which is bad because the fish wouldn't be able to breathe, then they would die off, then the bacteria would decompose the dead fish, which would further decrease dissolved oxygen levels and so on. Phew...
By the way, do you know which chemical you would use to kill the weeds?
Your F&W might be able to help you out to. The carp might be a good idea as long as they dont eat all the vegetation. Better ask an expert about what to do just to be sure. Good Luck