Question, is it something that is happening without you noticing? I ask because there is a person that I am working with right now that has it (all the time), he really does not notice it (he was never without it, so he does not know the difference) unless it is pointed out or he just happens to think about it. He is just like you in that it does not matter what poundage he is using. Many people believe he is over-bowed or offer all kinds of different advice, which is not helping him.
I would suggest finding out if there is medical reason.
Before the next time you go for a checkup tell the Doctor your problem and ask for an Electrolyte analysis. This is easily fixable. If there is an imbalance they may recommend supplements such as magnesium. If it is neurological, there is not a lot to do, but don’t be too concerned.
Many coaches believe that this quiver will not be much of a detriment to shooting ability at all. Strength training can help to a point along with biomechanical movements and alignments. Also FWIW, there is a Resident Archer at the Olympic Training Center right now that has this.