A peripheral stabilizing system for elevated flooring surfaces that is configured to resist uplift forces acting against the elevated flooring surface thereby reducing the likelihood of dislodged surface tiles and the like. Broadly, the disclosed system includes a support structure disposed over a fixed surface (e.g., roof deck or the like), a plurality of surface tiles appropriately laid over the support structure, and one or more restraint apparatuses (e.g., support ledgers) that are positionable adjacent the outer periphery of the flooring surface. Each restraint apparatus includes a mounting portion that is securable to a wall (e.g., parapet) and a restraint portion positionable over a portion of the elevated flooring surface adjacent the outer periphery for restricting movement of the flooring surface in a direction away from the fixed surface.