From your circuit, by adding sources in parallel, you didn't increase the current going through the load but you DID decrease the current being pulled out of the batteries(compared to having a single battery). This is because the three sources, assuming they all have equal voltages when in parallel, does not increase the output voltage and with your load which we consider to be constant in resistance thus, it will not increase the current going through the load.
Basically, if you look at the math it looks like the current from the sources add up but actually you didn't add them up, you split them up into three.
If you want to increase current, either you increase voltage or lessen the resistance of the load.
Maybe this will help to understand adding sources in parallel and what happens to the current.
Multiple sources in parallel:
Multiple sources in series:
Hope this helps! Goodluck with your project :D