Weed kills (2-4D, glysphosphate, triclopyr, etc.) do just that... kill actively growing weeds. They aren't designed to offer weed barrier / block performance, in fact most are designed specifically to leave the ground safe for planting just 3 weeks after planting (or even less for Mesotrione).
As rgr33 already said, You need a weed block, preferably applied in March. This will form a mechanical barrier layer in the surface soil, to prevent new weeds from germinating. Generally called "pre-emergent" herbicides, usually purchased as granular, but also available as spray. If applying to gravel, I don't think spray is an option, as it will just sit on the surface of the gravel, never make it down to where the weeds are actually rooting and germinating... you probably want granular. These products are typically designed to block germination for 12 or 16 weeks, leaving soil ready for over-seeding in September when applied in March. In your case, you might want to apply 2x per year, just mind your yearly maximum thresholds, for ground water concern.