A media handling system includes a platform, a bin supporting the platform below and for undergoing movement toward and away from a sheet feeding position, a first motion transmitting assembly coupled between the platform and bin and tailored to counterbalance the weight of the platform and any stack such that as the weight decreases the platform is lifted toward the sheet feeding position to maintain the stack top below a lower limit position thereof, a control mechanism to sense the position of the stack top relative to a given range between the lower limit position to an upper home position, and a second motion transmitting assembly drivingly coupled to the platform via the first motion transmitting assembly and responsive to the control mechanism sensing to cause the first motion transmitting assembly to further lift the platform to and maintain the stack top position within the given range.