In short, VNO doesn't provide you any protection, it just tells you that flying that fast puts you in a regime where structural damage will occur before increased load factor will cause a stall -- regardless of weight.
For part 23 airplanes that are not turbine powered and VD has not been established, 23.1505(b) establishes VNO must be established such that it is between VC,min and 0.89*VNE. Section 23.335 defines VC as a multiplying factor of the square root of wing loading at design maximum takeoff weight. For normal and utility category airplanes, VC is design cruising speed and is be between 33 √(W/S) and 0.9 VH where W/S is wing loading at the design maximum takeoff weight. The factor 33 may be scaled as low as 28.6 based on W/S values greater than 20 (the regs do not provide units on any of these numbers...). VH is the maximum forward airpseed in level flight at maximum continuous power at sea level.
Section 23.335 also defines VA and the only relation to VC is that VA need not exceed VC.
We can see from this information that establishing VNO is a design choice based ultimately upon maximum possible wing loading as a guideline and unlike VA stall speeds are not involved in the calculation.
What you can take from this is that VA will vary by weight (because this affects the stall speed) but VNO is based upon wing loading at max gross takeoff weight and is constant with actual weight.
Flying slower than VA you will stall before causing structural damage. Flying faster than VA you will cause structural damage before stalling the airplane. VNO will be at least the VA or higher. Flying below this speed doesn't really tell us anything (VA is better for that), but flying above this speed lets us know the design margins for load factor induced structural damage are such that we don't want bumps or abrupt control deflections because we can damage the airplane.
Regulation excerpts.
§23.1505 Airspeed limitations.
(b) The maximum structural cruising speed VNO must be established so that it is—
(1) Not less than the minimum value of VC allowed under §23.335; and
(2) Not more than the lesser of—
(i) VC established under §23.335; or
(ii) 0.89 VNE established under paragraph (a) of this section.
(c)(1) Paragraphs (a) and (b) of this section do not apply to turbine airplanes or to airplanes for which a design diving speed VD/MD is established under §23.335(b)(4). For those airplanes, a maximum operating limit speed (VMO/MMO airspeed or Mach number, whichever is critical at a particular altitude) must be established as a speed that may not be deliberately exceeded in any regime of flight (climb, cruise, or descent) unless a higher speed is authorized for flight test or pilot training operations.
§23.335 Design airspeeds.
Except as provided in paragraph (a)(4) of this section, the selected design airspeeds are equivalent airspeeds (EAS).
(a) Design cruising speed, VC. For VC the following apply:
(1) Where W/S′=wing loading at the design maximum takeoff weight, Vc (in knots) may not be less than—
(i) 33 √(W/S) (for normal, utility, and commuter category airplanes);
(ii) 36 √(W/S) (for acrobatic category airplanes).
(2) For values of W/S more than 20, the multiplying factors may be decreased linearly with W/S to a value of 28.6 where W/S=100.
(3) VC need not be more than 0.9 VH at sea level.
(c) Design maneuvering speed VA. For VA, the following applies:
(1) VA may not be less than VS√n where—
(i) VS is a computed stalling speed with flaps retracted at the design weight, normally based on the maximum airplane normal force coefficients, CNA; and
(ii) n is the limit maneuvering load factor used in design
(2) The value of VA need not exceed the value of VC used in design.
