LWR's don't just make plutonium in principle. A significant amount of energy produced by commercial LWR's actually does comes from plutonium fission!
While Plutonium-239 is weapons grade, when left in a reactor for more then a few weeks it will absorb another neutron, becoming Pu-240. Pu-240 poisons the fuel as far as weapons are concerned, its presence prevents the material from being used in a weapon.
If you had the technology to separate Pu-240 from Pu-239 then you could have more easily separated U-235 from U-238, which would be far cheaper since the Plutonium isotopes are closer together in mass, and come from radioactive fuel which was in the reactor.
So to answer your question - we aren't worried about other nations being able to make weapons-grade material with LWR's because it really isn't feasible, unless you stop the reactor to refuel it every few weeks instead of running it for 2 years. This kind of activity would not go unnoticed and would be expensive and wasteful compared to conventional methods (e.g. if you had the money to waste on a commercial-sized LWR to operate it with a capacity factor < 50% to refuel it all the time, as well as the fuel processing plant to get the plutonium out of the highly radioactive fuel, you could have afforded a small research reactor to breed plutonium to begin with).