Proximity Sensors / Mach3 not showing

[Jonathan]

The resistor is sized so that when the output switches to ground, there's only a few milliamps flowing through it.

I just ran the figures, and with a 4k7 resistor connecting 5V to ground, it's only allowing slightly over 1mA through, so you could use a lower resistance value.
Using a standard 1/8W resistor, you could go as low as 200ohm before resistor overheating becomes a problem. I'd personally opt for something in the 1-2K range, but it's not critical.

Resistor overheating isn't the limiting factor. With 200 ohms you'd have 5/200=25mA. The parallel port can (apparently) only source/sink about 14mA, hence to avoid damaging the port if connecting directly I'd use something higher. So I'd agree to sticking with at least 1k just to be on the safe side.