The　booming　of　multimedia　technologies　has　promoted　the　diversity　of　visual　big　data.　To　learn　common　features　across　heterogeneous　image　data,　the　image　co-processing　has　exhibited　its　advantages　over　the　separate　one.　Recently,　an　active　topic　of　image　co-processing　is　the　object　co-segmentation,　which　aims　at　simultaneously　extracting　and　segmenting　shared　objects　from　relevant　images.　In　this　paper,　we　address　this　problem　with　a　weak-supervision-based　probabilistic　model.　We　introduce　the　weakly　supervised　priors　to　alleviate　the　confusion　between　common　foreground　and　background,　thereby　facilitating　performance　improvement.　To　ensure　the　validity　of　potential　background　prior　knowledge,　the　nodes　on　four　sides　of　image　are　respectively　leveraged　as　the　labelled　queries.　After　that,　we　develop　quantitative　probabilistic　metrics　for　precisely　measuring　internal　consistencies　within　single　image　and　correlations　between　multiple　images.　Combining　the　intra-image　consistencies　with　the　inter-image　correlations,　we　propose　an　optimized　energy　function　coupled　with　binary　labeling　and　graph　connectivity　to　carry　out　the　object　co-segmentation.　Extensively　experimental　results　on　real-world　datasets　demonstrate　that　the　proposed　method　achieves　superior　co-segmentation　performance　to　the　state-of-the-arts,　with　a　significantly　reduced　time　consumption.