Balance screws can certainly be a pain if they snap off. And they can be small - the pocket watch sizes are not too bad to deal with, but the wrist watch sizes are worse...this is from a Cal. 321:
One screw head snapped off when I was adding washers during dynamic poising:
But I managed to file a small flat area on each side of the side that was sticking out on the inside of the balance rim, and use tweezers to turn it out:
Ladies watches are even worse...
Click to expand...