To clarify what Jarred mentioned, cleaning your filter will remove some debris before it adds to the bioload, but it's generally not a good practice to continually clean the filters that often as you may be removing the food source for the bacteria which will cause problems when you are not able to do a water change and cleaning right away.
Also, when he said clean it in tank water, he means removed tank water, not in your tank. That may be obvious, but it's good to add that. Syphon some water into a bucket, and rinse out the sponges in it.
I actually don't recommend cleaning any of the filters in anything but discarded tank water, because while it may not be the biological portion primarily, even sponges, carbon filter, and the baskets that carry them have useful bacteria on them.
Do your filter changing in shifts, one a week on different weeks. That will be fine.
If you have a problem with nitrates still with weekly water changes, you are more than likely overstocked. What size is this tank, what is in it, and what is your water change/cleaning regiment?