Ugh... How did you measure those 5.1V. Pin-to-ground, or on IC-Leg-to-ground?
Because a quick calculation shows, that:
a) a 2KOhm resistor at 5.1V should draw 2.5mA current, rather than 1.8
b) a 1KOhm resistor at 5.1V should draw 5.1mA current, rather than 2.6
c) a 500Ohm resistor at 5.1V should draw 10mA current, rather than 3.6
A small look at the fact, that at 1KOhm the current is half of what is expected points out an 'internal' 1KOhm resistance.
BTW. Time and again I found out, that pin 13 is called LED PIN, probably for a reason
Ohhh... I just took a look at the motor's data sheet. It may be too-much for ANY Arduino pin, and yet ANY Arduino pin may be too much for this motor.
The voltage for the motor is expected in the 2.5-3.8V (i.e. around 3.3V) with 70-80mA, but Arduino pins put up 5V (PWM pins too) up to 40mA. Why not use an H-Bridge, or at least a transistor switch with two diodes (to drop 1.4V) scheme to power the motor with 3.6V with higher amperage?