Recently,　duality　principles　in　g-frame　theory　were　studied.　This　paper　addresses　a　relaxation　of　g-R-duals.　We　introduce　the　notion　of　weak　g-R-dual　in　g-frame　theory　setting,　and　present　the　link　between　frame　properties　of　a　bounded　operator　sequence　and　its　weak　g-R-duals.　Using　weak　g-R-duals,　we　characterize　g-frames　and　(unitary)　equivalence　between　g-frames.　And　using　pseudo-inverse　operators,　we　represent　the　canonical　duals　of　weak　g-R-duals.　Some　examples　are　also　provided.