Motor Driver Circuit
This is basically Ohm's law at work.  You have a circuit going from your batteries, through a transistor, the motor's coil, another transistor and back to your batteries.  To know exactly what's going on measure the voltage drops across the components.

I can think of a few of things that could be going on:


You aren't driving the H bridge properly and the transistors in the bridge haven't switched properly.  So they look like a higher resistance in the circuit and measuring with no load (close to zero current) will show almost no voltage drop on them but once you hook up a load (higher current) you'll drop a lot of voltage on them.
You are overloading your power source (batteries) so your supply voltage is dropping under load.
Something the PIC is doing, what SW is it running?  Is it PWMing the motor?


Measure the voltage drop across the components (battery, bridge) and post the schematic and parts that you're using for a more detailed answer.