Curtain wall mullion anchoring systems for resisting dead load and negative wind load, and that permit three-way construction tolerance adjustments. The mullion anchoring systems include an anchoring device secured to a building structural element and attached to a mullion connection bridge, which is connected to a mullion connection clip, which is connected to a mullion. Uplifting forces on the anchoring device may be significantly reduced or even eliminated by transmitting dead load under negative wind load conditions from the mullion to the anchoring device at a point over the inside of a concrete floor slab, such that the dead load counteracts any uplifting force generated by the negative wind load.