This option may not be the best one for a rabbit who is overweight. A young rabbit may use both the litter and its food dish for both food and litter. However, if you always dump the soiled food out of the dish into the litter box, and clean the dish before more food is given, the rabbit will very quickly catch on. Rabbits will nibble at the food pellets in the litter box for awhile when they are fresh, but as the litter become soiled, they lose interest. Finally, some rabbits urinate or drop pills in their dishes as a matter of course.
Dribbles usually indicate a bladder infection.
Get your bunny to a rabbit-vet who will probably put her on an antibiotic. If the dribbling stops, you know that that was the problem. From the rabbit's perspective, urine is primarily waste material to be depostited in the litter box, but pills are a tool to be used to mark that territory that the rabbit believes it owns. It's a bit like a child going home and closing the door, because someone is calling her names. They may make the playground an unpleasant place for her, but they can't bother her in her own home.