The weave, in my experience is related to the width of the contact patch of the rear tire. The width of the contact patch is largely a product of the aspect ratio. IMO, for the Commando, a pointy shape is better than a round one. The bikes seem to like the rear tire to be only slightly wider than the front.
Following Jim C's point, right now I have the weave. Against better judgment but because of a super low price, I bought an Avon Super-Venom in a race compound, off ebay, for the rear of my Commando for only $100. The tire does have Avon's cantilevered side wall design so it fits my rim nicely but it still has a contact patch that is too wide, relative to the width of the front tire's contact patch. I now have the worst case of weave that my bike has ever had. I did not change the front tire too, so I do have too great a difference between front tire and rear tire width. I'll pull it off and stick it on my old '86 GSXR, where it's low round curve shape is perfect for the bike.
For my Commando, the weave always immediately goes away, if I move my weight/butt to the rear of the seat. Try going into a tuck, move your whole body to the rear. For me, this is not a total solution since I like to be forward while entering turns but, to avoid the weave, I have to stay back until the moment that I have to shift my weight forward for an entry.