I definitely have a weak left leg and sit with my weight to the right.
Great advice above if you are still young and fit - but if you are older and stiffer, as I was when I started riding in my sixties, it is worth looking at possible causes. Both riding and strenuous attempts to correct this through physio might only make things worse.
For most of us there is a natural degeneration of joints with age - the tissue that cushions the bones becomes more rigid or shrinks.With some people in the spine and others in hips and knees.
As the bones close in on your back they may squash or trap nerves -
Thus any RI attempting to get you straighter on a horse by asking you to put more weight in your left foot, or more weight on your left seat bone may cause you pain at the time, and or next day. And the more you the rider try to do as asked - the worse it may be.
Thus you need to start with possible medical causes and consider physio or pilates only in the light of that.
There are balance exercises on the Nintendo wi fit which some of us older riders here have found good.
On the riding side, one RI experienced in RDA told me she would shorten the stirrup on one side to help unequal riders. But she wanted to watch first how I rode with equal length stirrups and indeed I do best with stirrups of equal length.
So this is the next question. Are your stirrups at equal length?
An amazing number of riding schools have stirrup leathers that are odd or of unequal length on a horse - and then it is almost impossible for the teacher to adjust those stirrups for someone like you or me. I suggest you ask for matching stirrup leathers and make sure your stirrups are completely level before mounting - then ignore any crookednes in your own body. My crookedeness reduces over the course of a ride.
At the same time check your saddle is central on the horse. By riding crooked (which we cant help) we tend to shift the saddle and that makes things worse. At our school we may ride bareback - because sitting on a horse without stirrups or saddle helps to show exactly how crooked we are and whether or not things can be improved. It also focuses on balance. What is important is not the weakness of your leg - women riding side saddle use only one leg - but your balance on your seat in the saddle. Good balance is a matter of safety.
Once you have really looked in detail at your own physical set-up and looked at how you get on with stirrups completely equal, then you and your RI can make a judgement about whether or not it is bet for you to ride with one stirrup slightly longer than the other.