Two weeks ago I used weed killer on weeds in the rose garden, which has worked and they are dead.
What do I do next do I weed them out or digg them in?
Provided they are totally dead you can either leave them (as I do, decaying weeds get recycled) or remove them (as my OH tries to get me to do.). If you used glyphosate make sure the weeds have gone yellow / brown before lifting them.
either i would remove them but if its a large area this can be a bit tedious so for a large area i would dig them in
If they are close to the roses, I would carefully loosen some soil near by and bury them.