I believe that the Kwikset will fit in the Weiser, but the Weiser is thicker along the top of the key and will not fit into the Kwikset, if someone can confirm.
A KW1 key will fit into a WR3/WR5 keyway, but the depths/spacing are different between these manufacturers. There is also a WR6 blank which has the traditional Weiser square bow but a KW1 keyway.
you can copy a factory weiser key onto a kwikset blank and it will work, but not well. you only ever want to do this if you have say, 3 weiser locks on your house and 1 or 2 kwikset locks. There is a lot of play in a weiser lock, about 1-1.5 depths per chamber depending if you lift up on the key or push down.