Does the wattage of a resistor factor into the resistance of a resistor?
The size or surface area of a resistor is not related to its resistance.  It only determines the resistor's power-handling ability.

A 1000 Ohm resistor will measure 1000 Ohms and have the same effect on current in a circuit regardless of its physical size.

Edit: For most resistors, what you see is mostly just a package that protects or covers the actual resistor element.  However, the actual resistor element for a high power resistor will be much larger than one for a low power resistor.  The resistance is determined by the resistivity and dimensions of the resistor element - a 1000 Ohm 1/4 Watt resistor will be made with a higher resistivity material than a 1000 Ohm 10 Watt resistor.