Starting this thread as a clearing house for discussion of space weapons. Primary emphasis will be on space-to-space and space-to-surface weapons, but surface-to-space may also be considered. To start...
The Lubin UCSB laser propulsion system efforts have been funded by Breakthrough Starshot for $100 million. They are working working to demonstrate proof of concept for light-propelled nanocrafts.
A large scale network of several 70 Gigawatt lasers on Earth, Earth Orbits, the moon Mars and asteroids is not as distant as one might think because of several converging systems and technological shortcuts.
It looks like we could get 100 kilograms to 2% of light speed and 10 tons to around 0.3% of light speed, or 1000 kilometers per second. That would be a solid tungsten cube 80 centimeters across (no need to be aerodynamic in space). The kinetic energy would be on par with a large thermonuclear weapon (around 1-2 megatons) which should be enough to put a giant hole in any ship that's not either insanely huge or armored with exotic matter.
This could be the main gun of a space battleship.
As for a secondary gun, it could be a miniaturized nuclear Verne gun. It's not capable of relativistic launch speeds, but you could use it to build a giant nuclear shotgun that launches hundreds of tons of metal shards at close range to destroy fighter swarms and lightly armored ships.