How to measure the maximum weight that a DC motor can move?
"The salesman told me ..." LOL!  If physics was his thing, he'd probably not be a salesman.  In any case his job is to make a sale, whether you get your device working or not.

The first thing you need to decide is how much power the motor needs to have.  You can then worry about torque and speed later.  Those can be traded off against each other, but you can't cheat the physics that requires a certain power for certain tasks.

There are two end-user criteria you need to look at to decide the power.  These are how fast you want to be able to accelerate, and what minimum speed you want to be able to go up a decent hill.  I'll use the hill criterion as example.

Let's say you want to be able to go 20 MPH up a 20% grade.  20% grade means you go up 1 part for every 5 forward.  Since the only physics work being done is going up, the problem reduces to raising 350 kg straight up at 4 MPH.  4 MPH is 1.8 m/s, and here on earth 350 kg weighs 3.43 kN.  The power expended is therefore:

&nbsp;&nbsp;(1.8 m/s)(3.43 kN) = 6.13 kW

Of course there will be some friction to overcome, so you'd want about 10 kW in this example.  Since 500 W isn't even close, you either have to specify much lower performance or get a much bigger motor (and the power source to feed it).

Let's flip this around and see what 500 W can do.

&nbsp;&nbsp;(500 W)/(3.43 kN) = 146 mm/s

That's how fast 500 W can lift the whole unit straight up.  Applying that to a 20% grade, for example, it can move along at 5x that, or 730 mm/s, or 1.63 MPH.  In reality there will be friction and other losses, so probably not more than 500 mm/s = 1.1 MPH.

Added about torque

You should start with power as described above.  Once you have decided how much power the motor must put out, you face the torque/speed tradeoff.  You can figure out what torque/speed you need at the wheels, but that will usually be much too slow and too high torque for a reasonable electric motor to produce directly.  As a result, there will be some gearing between the wheel shaft and the motor shaft.  Since gearing is in there anyway, pick a good motor and then design the gear ratio accordingly, not the other way around.

To put this in perspective, let's look at the torque and speed required go up a 20% grade at 20 MPH as described above.  Let's say the wheels are 500 mm in diameter, so 250 mm radius, so 1.57 m circumference.  20 MPH is 8.9 m/s, so the wheel must turn at 5.7 Hz.  Your not likely to get a suitable motor with peak power and efficiency at 5.7 Hz (342 RPM).  You'll probably end up with a 5x to 10x gear ratio, depending on the best available motor you find.

For example, let's say you've decided you need a 10 kW motor.  That could come as 60 Hz (3600 RPM) and 26.5 Nm, 20 Hz and 80 Nm, or a variety of other combinations that all result in 10 kW.  Suitable motors will only be available in limited combination, and the gearing will likely be custom designed anyway.  Pick the motor, then let it dictate the gear ratio.