Output voltage of unity-gain buffer varying with current?
Resistors R1 and R2 set the output voltage of the LM317 to 11.7 volts.  However, the input voltage is only 6 volts, so the LM317 can never get anywhere near regulating.

The LM317, and other three-terminal linear regulators can only reduce the input voltage, not increase it.  In addition, they require a certain amount of headroom to operate correctly.  I recall (without looking at a datasheet) that the LM317 requires the input voltage to be at least 2 volts above the output voltage in order to regulate.