Strange op-amp circuit using LM324
The output of your opamp is not rail to rail. Checkout the datasheet, first page:


  Large Output Voltage Swing 0 V to V+ − 1.5 V


If you have a look at the schematic you see a darlington high side output stage, Q5 and Q6, in series with a short circuit protection resistor, Rsc.

Since the base of Q5 can't be higher than 3V, if the transistors are in the linear region you get two Vbe drops to the top of Rsc, which is about 1.4V, then the drop on Rsc, depending on the load current.

You were lucky to get up to 2V, actually, and the transistors were barely on.The minimum output current is 20mA, try to add a 100Ohm resistor as load and see what happens.