QED is right, a diagram or description (or even a patent number) would help, but I interpret that sentence differently than he did.
In the context of a standard balance, it would make sense that “the imaginary plane of the fulcrum” would be the vertical plane containing the balance arm, weighing pans, and fulcrum – i.e. the plane perpendicular to the axis of the fulcrum, not a plane containing the axis. It could make good sense to assure the weight is in this plane to assure that the weight is reasonably balanced in the pan, rather than exerting an off-center (lateral) force or torsion. I can’t imagine placing weights on the plane of the axis around which the fulcrum turns: the fulcrum generally turns toward or away from the weight, and by definition, that is perpendicular to the axis.
This also has the advantage that “the plane of the fulcrum” is uniquely defined. There is only one plane perpendicular to a line, but there are an infinite number that contain a given line. Absent any further specification, I’d expect the Patent Office to request clarification before granting the patent
Of course, since you’re looking at patents, I presume that the inventor had some clever non-standard device design (and I’ve seen plenty of those) so all bets are off.