If I cook a hot dinner on a canister stove and plan on cooking a hot breakfast in the morning, can I leave the stove on the canister overnight or would it be better to take it off and reattach in the morning?
No, go ahead and leave it on, you'll likely save fuel that way, be it a very small amount, but you do lose some fuel each time you take the element off of the canister. You don't need to take it off if you're not packing it away.
My experience is with portable grills and cooktops. They're a bit different, but close enough that I think this may be informative.
The valves on cheaper ($50-200) camping grills aren't the best. I've owned two that still put out some gas when they're "off". If you take the whole valve out of the grill and hold your hand over the pinhole, you can feel a small breeze.
I usually leave the canister attached if the grill is staying outdoors, but I unscrew the canister if the grill is going in my basement.
After unscrewing the canister, put your hand over the valve and feel for a breeze. I've had canisters that their internal valve doesn't close after unscrewing. Just pay attention and screw it back onto the grill and rely on the grill's valve.