I've read several Lie Nielsen plane owners say that having a heavy plane is an advantage, as in having the momentum of a heavier plane help push the plane thru the cut.
Here's a modified Millers Falls to make it heavier, notice the small weights precisely for tuning the balance, and the high tech hot glue adhesive.
plane weights 3.jpgplane weights 2.jpgplane weights 1.jpg
btw if you want to try this at home be sure to clean the dead bait of of the fishing weights otherwise this idea really stinks.
Happy April 1
and no, i didn't try to plane with it, and no planes were harmed.