A Treble for me is: loop (chain) on the hook already then wool over to make a second loop then through the stitch below hook wool through making 3 loops on hook then hook wool and through 2 loops then hook the wool and through 2 loops...that's my Treble!
But looking l think that's your Double?...
The yarns l've used for the sock/slippers is about equivalent to USA worsted so l'm told but l use anything to hand and double/treble up on strands and always do a small sample to find out how many stitches to the inch anyway
The wrist warmers and sock/slippers are exactly the same pattern really it's just the slippers have a sewn up toe and the wrist warmers have a finger loop
Used the same weight of yarn but changed the size of hook to make the slipper/socks bigger and they fit my OH and he has size 9's