From Wikipedia Cantilever wings require a much heavier spar than would otherwise be needed in cable-stayed designs. However, as the size of an aircraft increases, the additional weight penalty decreases. Why? The article does not have a citation there.
I think the Wikipedia article is wrong. Scaling the structure has other issues, but spar weight is not one of them.
The correct approach is to compare the scaling-up of a cantilevered monoplane wing with the same scaling-up of the equivalent wire-braced monoplane design.
In both cases, structural weight rises with the square of the linear scaling, for example doubling the length and span will give a fourfold increase in structural weight. The designer's challenge is to maintain the same weight of structure per unit of wing area, called wing loading, at scale.
The real difference comes not with scale but with speed. As the speed rises, the drag of the bracing rises more sharply, while the aerodynamic forces on the wing demand a stronger structure, especially thicker skinning. Eventually you reach a point, at around 200 mph (300 kph), where the drag of the bracing becomes excessive and the strength of the airframe will admit a cantilever construction without excessive additional weight penalty.
This was what triggered the historic change in design habits which the Wikipedia author was trying to explain and is, I suspect, what they would have said had they known better.
I have now substantially reworked that section of the Wikipedia article (current version here) and added a couple of citations.
Interesting, because the largest bridges are cable stayed. Any design depends on anticipated G loading and top speed. Not sure if this "engineering by rote" maxim belongs in anyone's concept toolbox.
Stayed cable designs suffer from increased drag with increasing speed, but the major penalty is the inefficiency of 2 wings compared to one, and the further penalty of having to carry a heavier, more powerful engine for similar cruise performance, with another penalty of having to carry more fuel to get the same range.
Larger planes are generally not designed for fighter plane-like G loading, and a slightly heavier internal spar on a more efficient single wing become advantageous.