Comparative form of grabby; more inclined to grab things or take what isn't offered.
From English 'grabby' (informal, meaning grasping or selfish) + '-er' (comparative suffix); modern colloquial formation.
Children naturally become grabbier around age 18 months, which psychologists call the 'mine!' phase—it's not rudeness but a developmental stage of understanding ownership.
Complete word intelligence in one call. Free tier — 50 lookups/day.