The main obstacle that any country faces in trying to develop nuclear weapons is acquiring the fissile material that is used to make the bomb. That's the plutonium or highly enriched uranium.
The chemical process, called reprocessing, is used to deal with radioactive waste in some countries. Canada does not do it, though it did in the past, in the 1950s. What it does is separate out the uranium and plutonium from the other radioactive fission products that are produced in a nuclear reactor through the fission reaction that happens there. When it separates, it becomes much easier to take the plutonium away from it. Any process that deals with the spent fuel is typically aiming at reducing the radioactive barrier that prevents people from being able to use it. That is the main connection.
Look at the Cirus reactor that Canada supplied to India. The way that India managed to produce plutonium for its 1974 nuclear weapons test was through this very process in spent fuel from the Cirus reactor.
In the science like the Moltex reactor's, they want to use a fuel that includes plutonium. Therefore, they have to do some kind of reprocessing prior to that.