As Peter mentioned unless it is a single cell stack its not the best idea. I did this once as an experiment and looking like I was taking on water on one side- listing to Port. But if you want try it in the pool and see how it feels. The benefit to pushing it up the right side is it keeps it close to your body. The further the object is away from you the more you will feel it in the water when it is a negative weighted.
If you are starting to wear doubles I seriously suggest taking an equipment configuration class for technical divers. In this class they go over all the aspects that you are having questions about. Steel tanks, Aluminum tanks, lights, backplates, harness, etc. etc. A few organizations have such classes and they are worth the time. It helps to transition divers from recreational to technical.
Weighting options- I am just worried that someone might think that they can ditch weight at depth to get themselves out of trouble. This promotes more problems as the diver approaches the surface and can no longer control their ascent rate. So if we take this a step further then we should not be using easy ditchable weights with things like Velcro holding them together. My buddies know never to ditch my weight- period. I weight myself at 15ft with 500 psi in my tanks, and no air in my wing. That reduces the weight and wing profile to what I need and keeps me from being over weighted. This can be done in a pool also.
I might of spoke out of line earlier about weight pockets. I see this trend that people think that they can ditch their weights and swim to the surface. This is really a fallacy when we start to dive with doubles. When we have doubles, lights, reels, drysuit, and decompression obligation dropping weight is not acceptable. So why would we want a system that is designed to drop the weight in the first place? I tend to wear the same drysuit/wetsuit for my doubles so the weighting is the same and at most I might put trim weight on my harness belt. With steel tanks this is a mute point. So really you use hard weight, or get a simple weight pocket that you could slide on. Any weight that I apply is for trim only at the waist. I try to put almst all of my weight in that v-weight-between my tanks. Just take care with those weight pockets and make sure they are not overweighed and might drop the weight. Aluminum tanks go positive and you are wearing two tanks plus your weight needs; is going to add up. Thats why many divers go to steel tanks.
Regards, Andrew