As per the link, 531 is stronger steel so can be built into thinner tubes retaining the same overlall frame strangth.
The weight difference is a bit complicated as it depends on what the butting is on the 501 and 531. All steel have the same density.
For example 531ST main tubes are 1 m and 0.7 m with the butting. But 531C was 08mm / 05mm. So 531C was approx three quarters the weight of a 531ST frame?
501 single butted was 1mm / 08mm and double butted 0.9mm/06mm according to the Reynolds tube constructors guide. So DB was weaker but lighter than SB.
In fact 501DB would only be approx 20% heavier than 531C, so pretty light.
I think 501 was just Cr-Mo, so in which case has a tensile strength of 85,000-115,000 PSI (590 - 760MPa). I believe 531 is around 120,000 PSI, so about 20% stronger than 501.
Reynolds claim 631 has strength of 850MPa and 853 1400MPa.