Awful title!
I have an animation object which animates the player, as well as a Motor6D weld, it works great with Roblox tools. In my new game I’d like to reuse the animations, but its no longer a Roblox tool, so the weld doesn’t work automatically 
Any help to sort this issue would be greatly appreciated!
When you are ‘equipping’ the gun, is it in the player’s character model? I’m pretty sure you can use Motor6D’s on non-tool weapons. I made this animation with a tool model, and in order to rig it I created a Motor6D with the RightHand as Part0 and Handle of the gun as Part1. Then I rigged the Magazine to the Handle using a Motor6D aswell, since it was part of the animation. When I played the animation it worked fine.
https://gyazo.com/03e88594aa389e9194e2ff0c025373e2
I don’t know how exactly your gun system works so I can’t really help beyond that.
You will have to change your animation slightly (either add a model that acts as a pseudo tool container or animate it again so it works without a tool) if you move it from a Tool instance to something else. Animations are pretty explicit in their instructions. I once had an issue with animation handles not moving but only arms moving, simply because the name of a brick was different.