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Granted the drawing is quite exagerated, but to make the point...
Build your bridge as in "A" and yes, there will be a horizontal component that will cause it to slide toward the lower side and some sort of support will be needed to counteract that force.
Build your bridge as in "B" and NO, there is NO horiontal component, nor more weight on the lower pier than the higher one. There is NO sideways force if the bottom of the bridge at the support points is parallel to the Earths surface.
Build your bridge as in "A" and yes, there will be a horizontal component that will cause it to slide toward the lower side and some sort of support will be needed to counteract that force.
Build your bridge as in "B" and NO, there is NO horiontal component, nor more weight on the lower pier than the higher one. There is NO sideways force if the bottom of the bridge at the support points is parallel to the Earths surface.