Grand Papa Bear Reupholstered  

Maybe the welt was cut on the cross grain because it was twill fabric, which has more give.  I dunno.  
One of the functions of welt is to serve as a bumper on parts of the chair where there will be more wear, and bias-cut welt will hold up better simply because there aren't any single, long threads of the weave being subjected to the most abuse.  
The other thing is that bias cut welt will handle curves with a minimum of ripples--providing the fabric is cut on the true bias.  If it's a bit off it could end up looking as twisted as rope even on the straightaways.  But twill is a diagonal weave to begin with so it's probably more forgiving.  
Did you do the orange cushions in the background, too?  That's a lovely sectional.  

I am simply amazed by the talents that you all seem to have...and I lack.
 
Drinks are on me.
 
Aunt Mark

Beautfiful Leif
 
Congratulations, and my upmost respect! 

Spanky: I've reupholstered everything in my house. So, yes the sectional (it is red in proper lighting).  And the yellow sofa. 
Mark: you are discounting your great sartorial photogenic talent. 

Spanky: I was curious about the welt. So I checked a number of photos of Papa Bears with original upholstery.  Not a bias cut welt amongst them. Not an enormous sample, but I suspect that it was done with the grain along the selvedge.

Huh, you're right about the welt. I wonder why they did that---it doesn't seem like it has any real affect on the finished look and I can't imagine that conserving yardage was that important on a high end chair like this...?
Anyway, the wear shown in the photo below is exactly the kind of thing that bias cut welt helps minimize.

I think the welt was done along the grain for a clean line around the perimeter of the chair.  
Cut on the bias, you can go 77 inches before you have a seam, which creates a bump, even when done properly as a diagonal seam. The chair needs 11 feet of welt, which puts the seam near the middle of the top arc. Not a pretty place for a bump. 
Any other arrangement requires two seams, and there isn't any good place for even one seam. The whole perimeter is very visible. 
As a high end chair, it might look worse to have ugly seams in the welt, making a continuous piece more desirable.

Ah, that may be it.  Though if you just trim the welt cord away a bit, the seam allowances will not add any bulk.  And if the seam is stitched accurately, the seamline itself will pretty much disappear (some fabrics are more obliging than others).  
I spend way too much time doing stuff like this, but I do really get a kick out of detail work.  Like hand stitched seams---I could do them all day long.  But if I have to do too many box cushion covers in a row I want to shoot myself.