The　emerging　Space-Air-Ground　Integrated　Networks　(SAGIN)　empower　Mobile　Edge　Computing　(MEC)　with　wider　communication　coverage　and　more　flexible　network　access.　However,　the　fluctuating　user　traffic　and　constrained　computing　architecture　seriously　hinder　the　Quality-of-Service　(QoS)　and　resource　utilization　in　SAGIN.　Existing　solutions　generally　depend　on　prior　knowledge　or　adopt　static　resource　provisioning,　lacking　adaptability　and　resulting　in　serious　system　overheads.　To　address　these　important　challenges,　we　propose　THOAS,　a　novel　Traffic-aware　lightweight　Hierarchical　Offloading　framework　towards　Adaptive　Slicing-enabled　SAGIN.　First,　we　innovatively　separate　SAGIN　into　Communication　Access　Platforms　(CAPs)　and　Computation　Offloading　Platforms　(COPs).　Next,　we　design　a　new　self-attention-based　prediction　method　to　accurately　capture　the　traffic　changes　on　each　platform,　enabling　adaptive　slice　resource　adjustments.　Finally,　we　develop　an　improved　deep　reinforcement　learning　method　based　on　proximal　clipping　with　dynamic　confidence　intervals　to　reach　optimal　offloading.　Notably,　we　employ　knowledge　distillation　to　compress　offloading　policies　into　lightweight　networks,　enhancing　their　adaptability　in　resource-limited　SAGIN.　Using　real-world　datasets　of　user　traffic,　extensive　experiments　are　conducted.　The　results　show　that　the　THOAS　can　accurately　predict　traffic　and　make　adaptive　resource　adjustments　and　offloading　decisions,　which　outperforms　other　benchmark　methods　on　multiple　metrics　under　various　scenarios.