An unpowered, manually operable apparatus for dispensing cushioning wrap material, the apparatus comprising: a frame; a roll of interleaf material rotatably secured to the frame; a roll of expandable sheet material in an unexpanded form rotatably secured to the frame adjacent the roll of interleaf material such that respective longitudinal centerlines (C1, C2) of each roll (14, 18) are substantially aligned; and a tensioning assembly (60, 70, 80, 90) operably associated with the roll of expandable sheet material to control rotational resistance thereof, wherein the rotational resistance causes the expandable sheet material to expand in length and thickness as it is pulled with the interleaf material manually by a user; wherein the frame comprises a pair of opposing supports extending upwardly from the frame to which the roll of expandable sheet material is rotatably secured; wherein the roll of expandable sheet material comprises a hollow, axially-extending core; and wherein the tensioning assembly (60, 70, 80, 90) comprises: an elongated rod that extends through the hollow core, the rod having opposite end portions (60a, 60b), each end portion (60a, 60b) secured to a respective one of the supports; a first core plug attached to one end portion of the rod, the first core plug comprising opposite first and second end portions (70a, 70b), and a radially outwardly directed flange adjacent the first core plug first end portion, wherein the first core plug second end portion extends into one end of the hollow core; a second core plug attached to an opposite end portion of the rod, the second core plug comprising opposite first and second end portions (80a, 80b), and a radially outwardly directed flange adjacent the second core plug first end portion, wherein the second core plug second end portion extends into an opposite end of the hollow core; and an adjustment mechanism operably associated with the second core plug that is configured to exert a compressive force on the roll of expandable sheet material to thereby control rotational resistance of the roll of expandable sheet material. a frame; a roll of interleaf material rotatably secured to the frame; a roll of expandable sheet material in an unexpanded form rotatably secured to the frame adjacent the roll of interleaf material such that respective longitudinal centerlines (C1, C2) of each roll (14, 18) are substantially aligned; and a tensioning assembly (60, 70, 80, 90) operably associated with the roll of expandable sheet material to control rotational resistance thereof, wherein the rotational resistance causes the expandable sheet material to expand in length and thickness as it is pulled with the interleaf material manually by a user; wherein the frame comprises a pair of opposing supports extending upwardly from the frame to which the roll of expandable sheet material is rotatably secured; wherein the roll of expandable sheet material comprises a hollow, axially-extending core; and wherein the tensioning assembly (60, 70, 80, 90) comprises: an elongated rod that extends through the hollow core, the rod having opposite end portions (60a, 60b), each end portion (60a, 60b) secured to a respective one of the supports; a first core plug attached to one end portion of the rod, the first core plug comprising opposite first and second end portions (70a, 70b), and a radially outwardly directed flange adjacent the first core plug first end portion, wherein the first core plug second end portion extends into one end of the hollow core; a second core plug attached to an opposite end portion of the rod, the second core plug comprising opposite first and second end portions (80a, 80b), and a radially outwardly directed flange adjacent the second core plug first end portion, wherein the second core plug second end portion extends into an opposite end of the hollow core; and an adjustment mechanism operably associated with the second core plug that is configured to exert a compressive force on the roll of expandable sheet material to thereby control rotational resistance of the roll of expandable sheet material. an elongated rod that extends through the hollow core, the rod having opposite end portions (60a, 60b), each end portion (60a, 60b) secured to a respective one of the supports; a first core plug attached to one end portion of the rod, the first core plug comprising opposite first and second end portions (70a, 70b), and a radially outwardly directed flange adjacent the first core plug first end portion, wherein the first core plug second end portion extends into one end of the hollow core; a second core plug attached to an opposite end portion of the rod, the second core plug comprising opposite first and second end portions (80a, 80b), and a radially outwardly directed flange adjacent the second core plug first end portion, wherein the second core plug second end portion extends into an opposite end of the hollow core; and an adjustment mechanism operably associated with the second core plug that is configured to exert a compressive force on the roll of expandable sheet material to thereby control rotational resistance of the roll of expandable sheet material.