Not enough power going through IRLZ44, activated by Arduino
What do you mean "4.5v through my IRLZ44"? Do you mean "4.5V across the drain and source? When the mosfet is switched on, the drain to source voltage should be extremely low (millivolts). When off, the drain to source voltage should be 7.2V. If it is less than 7.2V when off, the mosfet may already be fried, and the drain to source may be partially shorted.

Check the gate voltage. It should be above 2V (peferably above 4V) for the mosfet to work properly. Also, there needs to be a high value resistor from gate to ground, for the mosfet gate capacitance to discharge when it is switched off (otherwise it will not switch off).

Decrease the value of the 1K resistor to the minimum required to not go over the arduino pin current limit. Operating the mosfet in the linear region with a lower gate voltage may shorten it's life.