Before you can perform any exercise properly you have to get set up correctly. For a standing curl, a commonly overlooked aspect of proper setup is foot placement.
Most people keep their feet side by side, which creates a small base of support in the sagittal plane (front to back). That's a problem because the curl is performed in this plane. And when the barbell moves in front of you as you curl it, it causes your center of mass to shift forward.
To adjust for that, you have to lean back to keep from falling forward, especially if you're going heavy. That's all fine, but when you string a few reps together it forces you to swing the bar up and down, reducing muscular participation.
So instead of keeping your feet side by side, stagger them just a little bit, distributing your weight evenly. Like this:
This provides a bigger base of support in the sagittal plane that allows you to counterbalance your center of mass moving back and forth. Now you don't have to lean back and can maintain your posture.
It doesn't take a lot of stagger for this to work. Placing one foot just in front of the other, heel to toe, should be plenty. More stagger isn't always better though. It can become distracting and difficult to keep your posture and balance in the frontal plane (side to side).
Placing the toe of your front foot in line with the bar when your elbow is flexed to 90 degrees should be sufficient to make sure your center of mass will always be within your base of support.