SWR is really the ratio of reflected power to forward power. The ratio is the same regardless of output (unless your output is a few kilowatts and you set fire to the antenna). Typical SWR meters have a calibration control that you're supposed to set before taking an SWR reading. You need to set that calibration control each time, particularly as you raise or lower the radio's output power.
There are some SWR meters that can auto-calibrate themselves (the one built into my Kenwood TS-850 is like that), but I don't know if you have one of those.
If your meter has an "SWR/CAL" switch on it, key up the radio, set the switch to "CAL" and then adjust the calibration knob until the needle is sitting exactly at the end of the meter range. Then set the switch to "SWR" to see the actual SWR reading. If you were to, say, lower the radio's output from 5 watts to 2, the needle won't deflect as far when the meter is in CAL mode. You'll need to adjust the calibration knob again to bring it back to the end of the meter range before the SWR setting shows an accurate reading again. It should be the same as it was for 5 watts.
There's usually a minimum amount of forward power required in order to get the needle to reach the calibration point. The ones from Radio Shack are designed for CB radios, so they'll work ok with 4 watts of output. Others may require a bit more. (I have a Kenwood SWR/power meter that needs about 15 watts in order to take an accurate SWR reading.)
-Bill