I don't know about the swaying, but I do know it's probably a good thing for your mental health to not be addicted to anything. So the fact that you're 2 weeks in to stopping smoking weed, that is worthy of a big congratulations on your self control.
BIG CONGRATULATIONS!! Keep going. You are being good to you.
It may be that you feel sensitive to things in a different way now? I know when I stopped drinking caffeine, my energy levels were affected and it took weeks to re-stablise. And whenever I drink caffeine again, my energy levels get much more affected, I'm a lot more sensitive to it now. And it takes ages to re-stableise again, back to square one.
When I'm dizzy, I drink water and make sure I eat enough, and rest. Dizziness can happen from all sorts of things, most of them totally harmless. I think the bigger deal is that you're not smoking any more, and if this is a side effect, BRING IT ON, you can handle this, it's showing you that you've made the change and your body is adjusting.