My 2012 XT660R has suddenly developed a wobble tendency at highway speeds (100-120 km/h actual), and I am somewhat puzzled. I bought the bike new, it now has 8500km (5300-ish miles) on it, never been jumped, wheelied or crashed. The tyres are still the stock ones (Metzeler Tourance), with the rear clearly squared off due to highway commute, but the front looks fairly smooth. There is still at least 3 mm tread left on both tyres.
The front end feels OK in other respects, no imbalance, bearing noise, dragging or pulsing brakes etc. However, the suspension is defintely softer now than when it was new, and I suspect the front has sagged a bit.

Is it possible that the rear tyre is the culprit? It has been getting gradually more squared off, but the wobble has appeared more recently.

All advice is welcome, as I have not encountered such a problem before on my other bikes.