As a tyre ages, many things can happen to make it go out of balance. These might include:
1) Going out of round - quite common
2) Developing a bulge
3) Tread separation
4) Balance weight falling off!
5) Tyre damage
6) Wheel damage
etc, etc

So, before you worry about getting your suspension set up and/ or overhauled, I would get that worn tyre replaced and the new one properly balanced. The price of a new tyre doesn't pay for much suspension work!

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Cheers, Neil