Your last paragraph is the key one: Yes, there industry standard tests, and they were able to rate it for 180kg by passing those tests. You can do theoretical calcs until the cows come home to make sure you pass those tests first time, but you must undertake and pass these tests prior to adding a rating sticker or you open yourself right up to liability.
I looked at BS EN ISO 1119-1:1999 "Walking aids manipulated by both arms - Requirements and Test Methods" Part 1: Walking frames
I have picked out some key points, but you should read the whole document (or local equivalent) yourself.
One walking frame shall be tested, through Stability, Static Load, Fatigue, and Static Leg-strength in that order.
Stability: Forward, Backward and Sideways tests have different tilt angls, then a vertical load of 250N is applied to the centre of the hand grips.
Static Load: A load of 1,500N is applied, with an additional 15N per kilogram of maximum user weight above the standard maxium of 100kg. You would need to test to 2,700N (+/-2%) to demonstrate equivalence
Fatigue: A cyclic load of 800N plus 8N per kg over 100kg (1,440 for equivalence) applied downwards on the handles, 200,000 times, slower than 1Hz.
Static Leg-strength: Applied to each of the legs in turn, applied a minimum of 10mm further out than the lower end of the leg, and directed towards the centre of the frame. done by removing the rubber foot, and putting in a tightly fitting plug up to 100mm inside the leg. Height adjustment of frame must be at maximum. The standard requires a loading force for this of 300N, applied gradually over 2s, and held for minimum of 5s. but it also recommends testing at 500N, to provide a safety factor "for reasonable foreseeable misuse".