I've never had any problem with a loaded Pan - but I rarely go above legal speeds anyway. I've had a few runs into triple figures in continental Europe fully loaded, without any sign of problems - mine was an 06 model.
But I have noticed - the bike can be skittish if the rear suspension has too much pre-load - due to the quicker steering it creates
Having a top box without a pillion can be problematic as the eddy from the rider sideswipes the top box from alternate sides.
Having a pillion with a top box creates a much smoother airflow past the bike and top box - the bike is more stable with a pillion !
An aftermarket larger screen will certainly create more of an eddy behind the screen than the OEM screen.
Passing trucks into a headwind or when emerging from the lee side of a truck in a cross wind, I will ride out wide and then counter-steer across the lane through the bow wave to create a lean in towards the expected wind as I pass the cab. If there is a sudden gust from the side, already leaning into the wind makes it so much easier to handle.
Worn tyres, dodgy bearings, tyres not designed for heavier touring bikes (they can squish too much), inadequate damping, stiff or notched steering head bearings can all contribute to questionable handling. But I find the worse culprit can be the road surface - worn carriageways resulting in troughs in the wheel tracks; longitudinal ridges caused by the machines which prepare the road before resurfacing - these become exposed when the surface wears down and throw the bike all over the place.
If it is something you are concerned about - eliminate the problems that might have been introduced by a previous owner. Go back to OEM tyres for example. The OEM spec are the Bridgestone BT020 F rated tyres - although the T30 GT and T31 GT tyres have been tried, tested and approved by Bridgestone for use on the ST1300 and ride very nicely. One good thing about Bridgestone is that they test their tyres specifically on the Pans -1100 and 1300. Also check out the bearings and slacken the front axle and then tighten it up again following the correct procedure. Not everyone knows what it is.
But the 2007 shouldn't have any weave problems - the weave was reported around 2003/2004 and since then the models have had design changes and modifications to the way in which engine and swing arm are mounted and secured. Although no one is saying that the modifications were introduced to address that particular problem ! 'Weave' might be a misnomer. When the tests were carried out after the death of a policeman, the tester reported that it - began to "shake violently" while travelling at high speed .... making it uncontrollable.
Just suggesting that maybe there is a different explanation for what you have experienced.