What happens when you increase current to a DC motor?
By adding a battery in parallel, you do not increase the current. You increase the maximum current that the motor can take. Nothing will happen if you add another battery in parallel and the motor isn't suffering from shortage of current. 

Keep in mind that than in Ohm's law, you have 3 variables: \$V=RI\$. In this equation, you can affect one variable by changing the other two. For a given motor, R is constant, so that means that one of two possible variables you can change is out. 

You can either set the voltage to some level, which you seem to be doing by using the speed controller, and let the current come from the equation or you can use a different type of speed controller which sets the current and lets the voltage come out as a result of the equation. 

So how is torque related to this? Well motor has what's called back electromotive force and the equation for the Ohm's law is actually a bit different:
$$I=\frac{V_{battery}-V_{back-EMF}}{R}$$
The greater the torque provided by the motor, the lower is the \$V_{back-EMF}\$, resulting in greater current through the motor. 

When current is supplied by a battery, the battery's voltage usually drops. The drop depends on the type of battery and the current. If the current is above what battery is expected to provide, you can expect the battery to have lower voltage than expected, to overheat, maybe even explode. If the current provided by the battery is sufficient, the voltage drop isn't going to be as big. 

So it's as I said in the first paragraph: If the batteries can provide sufficient current to the motor (and you test this by checking the current when motor should be providing maximum torque), then adding another battery won't affect the current or the torque. If there isn't enough current and you add a battery, you can expect increase in torque because the voltage supplied by the batteries will be higher.