Can I change the order of my weapons in Bioshock 2?

You can't change the order of the weapons, but if you hold the right bumper you'll see a radial menu of all of your weapons. Just tilt your left stick towards the one you want to select it immediately.

The left bumper will also bring up a plasmid radial.

Unfortunately, you can't rearrange the weapons/plasmids in the radial either.