We report a systematic study on strong enhancement of spin-orbit interaction (SOI) in grapheneinduced by transition-metal dichalcogenides (TMDs). Low temperature magnetotoransport mea-surements of graphene proximitized to different TMDs (monolayer and bulk WSe2, WS2and mono-layer MoS2) all exhibit weak antilocalization peaks, a signature of strong SOI induced in graphene.The amplitudes of the induced SOI are different for different materials and thickness, and we findthat monolayer WSe2and WS2can induce much stronger SOI than bulk WSe2, WS2and mono-layer MoS2. The estimated spin-orbit (SO) scattering strength for graphene/monolayer WSe2andgraphene/monolayer WS2reachesª10 meV whereas for graphene/bulk WSe2, graphene/bulk WS2and graphene/monolayer MoS2it is around 1 meV or less. We also discuss the symmetry and typeof the induced SOI in detail, especially focusing on the identification of intrinsic (Kane-Mele) andvalley-Zeeman (VZ) SOI by determining the dominant spin relaxation mechanism. Our findingspave the way for realizing the quantum spin Hall (QSH) state in graphene.