B737 First Officer reported on departure experiencing an AFT SERVICE light resulting in the flight crew diverting to the nearest airport where they landed safely.

Narrative

As we were on a takeoff roll from ZZZ runway XXR Taxiway 1 intersection the amber 'AFT SERVICE' light came on between 80-100 knots. I notified the captain about the caution light and cancelled the caution. We took off normally and proceeded with the ATC departure instructions. When the time permitted we addressed the SERVICE DOOR non-normal checklist. We notified ATC about the problem and stopped our climb. We requested priority handling. We received vectors and continued to complete the checklist. The checklist led us to a conclusion that we need to land at the nearest suitable airport which at the time was ZZZ1. We entered a hold and continued to burn off extra fuel as we coordinated with the company. We proceeded with a normal over weight landing.