The biggest way to lose weight... Ask the inspector to take his foot off the scale
We've never really had a problem with weight on the robot... In fact, most years it's the exact opposite! We always end up either significantly under weight, or spend some time figuring out how/where to add weight (2008 we had a 20lb steel plate bolted to the very bottom of the robot, 2009 we bolted steel plates outside of our cantilevered wheels to support the bumpers, 2010 and 2011 we were under weight - 2011 by quite a bit).
You need to consider weight with everything that goes on the robot - it's easy to "over-engineer" something by building it with bigger/stronger parts than are really needed. What's difficult is building something to be just as strong (and thus heavy) as it needs to be, and no stronger.