Thanks, Rob. I don't know weights, so I'm curious... Would my father's Agfa and Ilford papers be closer in weight to your Kodak "single weight" or your personal "double weight" papers. Judging from the empty boxes, the specific paper types are Agfa Portriga-Rapid PRN111 ("1", "2" and "3") and Ilford Galerie IG "1.1K" "2.1K" and "3.1K".
Most people during the period I was working used only two brands of paper for their businesses: Kodak and Ilford. Commercial printing, in the sense of advertising/fashion/commercial was done on white smooth glossy, simply because glossy displayed the widest range of tones and was the surface which magazines, books, all printed publications could best use from which to make their reproductions which started post-photography life via massive copy cameras on rails, the images lit with carbon arc lights and ending up at the end of the process as printing plates on a press. The last thing anyone desired was the intrusion of paper surfaces forming part of the reproduced image!
The world of the high street: hatches, matches and dispatches - was far removed from mine, and I suppose that was where funny surfaces found their sales - much as today with canvas.
The differences between Ilford and Kodak, in practical darkroom terms, was that Ilford's grade numbers worked out as a half-grade softer than Kodak's. In other word, if you had a negative that really needed the difference between Kodak Grade 2 and Kodak Grade 3, you could choose Ilford Grade 3 because it was just that bit softer in tonal reproduction. In reality, almost any printer could make the print without switching brand just by playing with more exposure and slightly less development.
To explain the meaning of grades: you began with Grade 0 which was as soft/flat as any paoer would let you print, moving upwards through Grades 2, 3. I can't remember if a higher (more contrasty) grade was made than 3, since I never had to use or buy it.
Your choice of paper grade was a function of the state of your negative. If your negative was too contrasty you would try the soft grades such as 1; normal-looking negatives would usually suit 2, and thin, underexposed ones could print better on 3, simply because the contrast inherent in 3 would better reveal/accentuate the smaller differences of density within the thin negative.
It all sounds far more complicted in writing about it than it ever was in practice. In practice, you soon learned how to expose and develop your negatives to give you
your ideal of normality. That was why it was so important to process your own shoots: how else could you know if you were consistently over- or under-exposing your images, or under- or over-developing your films? I almost never had to use papers other than Grades 2 or 3. I do remember that there was another brand of paper that was reputed to be very much more contrasty, but can no longer remember what it was, so sorry.
Muligrade papers, introduced by Ilford, were another game altogether, and I didn't play it (until long after I retired and started an amateur darkroom again, where I used the above stuff in its RC iteration, and hated the look. I soon closed the darkroom again). You bought a box of that Mulitigrade stuff and another box of filters, and instead of changing between paper grades you swapped filters to soften or to highten contrast. I stuck with what worked very well for me.
The difference between single weight and double weight refers only to the thickness of the paper on which the emulsion rests. It played no part in the look of the print, just its physical feel or presence when looked at as an unframed print.
The types of papers you listed above were never used by me, so can't offer any personal knowledge about them.
Ciao -
Rob