A drawing, schematic, sketch, or picture of your setup would be helpful, since Vgs is not necessarily equal to either the voltage gate-to-ground or source-to-ground.
You may not care about the voltage gate to source, but the mosfet does. If you load is connected to ground, then when the fet tries to turn on, the load/source junction will rise in voltage thereby decreasing the gate/source voltage and shutting the part off. I would assume (due to the lack of clarity of the connections in the OP) the voltages you are reading on the voltmeter is the fets happy medium between fully off and fully on due to the amount of gate-source voltage available.
Since the Fet acts as a switch, can you put the load on the drain side? This would keep the source pin grounded thereby (1) guaranteeing the gate voltage you apply is (2) the gate-source voltage seen by the fet and (3) by your voltage meter connected to ground.