The other day while practicing I broke a stick and the only one close by was one a little heavier than my 5A. So I grab it and kept  on playing. And it was kinda cool. The heavier stick in my weaker left hand seemed to carry better on my tom runs and single stroke rolls.

I've played in the past with the left stick backward which presents a MUCH heavier stick than what I am talking about. This stick was just a little heavier and felt great. I may stick with it (doht)

Any of you play with two different weight sticks?

I only use different sticks on one song, "Cherokee".  At 340 bpm, I need the lightest stick I can find to keep up on the ride.  

I do use a stick in one hand and a brush or rod in the other quite a bit.  For example, on some Latin stuff playing a clave pattern with a cross-stick and a standard guiro pattern with a brush works quite well in a jazz combo setting.

I went through a phase where I used two different sizes. I noticed that the kick and snare were much more prominent than the hihat/ride in pop/rock music, so I started using a bigger, heavier stick in the left hand. I did that for a few years, then got into a hard rock band where I ended up using the heavy sticks in both hands.

Like Joker suggested, I also mess around with rod/brush combinations, a favorite being a Vater Acoustick in my right, and a regular wire brush in my left. That's great for light pop/rock/country where you need to play quiet, but still want to "dig in" a little.

My motto in this area is whatever works!  

Generally not two different 'sticks' but I'll mix up sticks and rods, and rods and rutes, and sticks and rutes, etc

Yes! -  in a variety of combinations - whatever supports the music and the moment.

Billy G.