This is the technique i use to get a generally worn and dusty tire I think it applies to an average weathered aircraft that would operate from a paved area or a dirt/grass filed. It is a good base to if you need to really "muddy" them up for harsher conditions.
First up is painting the tire. Mount on a toothpick for easy rotation and a good out of the way hand hold. Paint the hubs and let them dry. For the tire I mix Testor's rubber flat black so the black just starts to take on the rubber color. Use a good pointed brush with long bristle to hold some paint. Thin it just enough that it will flow a tiny bit when the tip is touched to the rim. Once the sidewalls are done finish the tread. I have never needed to mask a hub and it's only 2 tire anyway. Road wheels on a tank??? Ok maybe a mask there.
Chalk pastels work great for the weathering. I use white, taupe, reddish brown, grey and black. Starting at the lightest color I rub my forefinger on the pastels. Work down the row and don't worry about getting it evenly coated. The more variation the better. Do the same thing on you thumb, but I usually leave off the black on that side.
Holding the toothpick, spin the tire between your fingers. Do the same thing for the sidewalls. For the side I like to put a couple of light specks of pastel on my fingers for a second spin to try and get a little variation. The final pastel application is with some of the taupe and a light spin of just the tread area.
The end result should look something like this. While it looks a bit "grainy" in the photo remember these are pretty tight close ups of a small tire. They look much better from a normal viewing distance. Unlike when I use the pastels for post shading and they are ground into the paint surface pretty good, these chalks are lightly applied and will come off with the normal handling of installation. A quick light spray of flat seals it in place. If it lightens the effect, just apply a bit more and seal again. I usually only have to apply the 1 time and have never needed to apply more than twice.
Here are a couple of example of the varied degree that can be achieved with this method.