How many watts am I allowed to pull through the Leonardo ground pins?

How many watts am I allowed to pull through the Leonardo ground pins? (the 2 pins next to each other on the "power" side of the board. I'm using both combined)
It would make it easier if I connect my motor to the ground pins of the Leonardo (because of location).
(The positive is coming from a relay).

From the Atmega 32U4 datasheet the absolute max is

DC Current V CC and GND Pins................................ 200.0 mA

...R

The pins are designated as 0V / GND as a reference to their 'potential'.
The power you can return via those pins is expressed as Watts (Volts x Amps), but this isn't really any use to you, as in reality that 'current' will be determined by the weight (thickness) of the copper tracks, and their ability to get rid of the heat...!

This also true for the 5V and 3V3 pins, except their limits are imposed by active components (the regulators). The cause of expensive white smoke and smells.

So, to answer the question in a slightly different way...
If you have a suirtable power supply that ties the 0V / GND pins of the Arduino to a common 0V rail, which is shared with your sensors and output devices. The current will flow 'outside', around the Arduino board, using the heavier rated common supply wires. The 0V pins are only there to make sure the Arduino knows where the 5V and 3V3 levels should be in relation.

This is why it's important - e.g. if you have a 12v motor, or 1W LED using a separate higher rated 'power' supply - to tie the 0V rails together (under almost all circumstances).
The higher power (W=VxA) will flow through the motor via relay or h-bridge, and not through the Arduino. There are other techniques to limit the current sourced - or sunk - through the I/O pins.

EDIT: To expand on Robin2's note...
If you're drawing 5A from an external supply to drive some device, it's probably not a good idea to return that current 'through' the Arduino 0V pins... use that external 0V/ GND rail to take the heavy load away, off the board

Robin2:
From the Atmega 32U4 datasheet the absolute max is
...R

I doubt that it's Hansen70's intention to route it through the microcontroller. I think that the two pins that he's referring to are those between Vin and Vcc and those are simply tied together on the board.

sterretje:
I doubt that it's Hansen70's intention to route it through the microcontroller. I think that the two pins that he's referring to are those between Vin and Vcc and those are simply tied together on the board.

To clarify: I want to use the 7.5 volts that I power the Leonardo with, draw 200ma of power using these 2 ground wires: see attached

You don't draw power from the GND pins.
My first long post explains how that works.
Read up on DC electricity. Voltage/current/electrons (choose one!) flow from one pole to the other. Typically the higher voltage is called a 'source', and the lower (often 0V) is called a 'sink'.
To make electricity flow, you draw current from the source, and dump it into a sink. (it can get a lot more complicated but this'll do)

0V/GND pins are merely a reference to determine the scale of other pins/voltages with respect to each other.
You could for example operate a 5V motor between 12V and 7V - a difference of 5V, but controlling it may introduce other challenges.

The actual board only needs 'one' ground pin - but many circuits & designs implement multiple pins for convenience.
Current should not flow through the Arduino in general - that's why there are drivers and application specific shields.