Op Amp High Side Current Sensing
The LM358 can can't really get down to the negative rail while sinking current, and your circuit has about 250uA flowing into the output.
Increasing the resistors to 100K probably helped quite a bit, but it still is limited.
Referring to the datasheet for the typical characteristics:

To get down to 50mV it can typically sink perhaps 15uA with a 5V supply @ 25°C, so maybe you can count on 5-10uA in realistic conditions. And that's just to barely get down to 50mV out.

To get something useful out of this, you can increase the gain significantly so the minimum output is (preferably) in the +1V range. But then you'll run into common mode range issues if you just increase R11/R12.