Did you measure the voltage between Vout and ADJ? It should be 1.25V. The voltage ADJ to GND should be near 0V.
What is your resistor value for R1? R2/R1 needs to be near 0 to get 1.25V output, so you should set R1 >> R2 (or ground ADJ directly).
I guess there's no problem with the resistors though, do you have an oscilloscope to check if the regulator is oscillating? Try adding a smaller value one (some nF) to the input and output (additional to the 1uF one).