As noted by Sweetcretin and others, the limiting factor is the plug and receptacle ends of the cords. They are rated at 15 amp if standard parallel blade ends, doesn't matter what the gauge of wire is, the lowest common denominator is the plug and receptacle ends.
I just picked up a small 16 gauge cord I have, and it has a shiny tag wrapped around the cord at the plug that says 10 amp. In this case, the wire is the lowest common denominator.
I have lots of extension cords, way more than I need. Some of the light 16 gauge cords, my Dad had bought to run a leaf blower, it worked fine on them, even several of them, doing gutters and the drive.
I have......
1 flat 50 ft 16 gauge (hate it)
3 round 50 ft 16 gauge (orange)
2 round 50 ft 16 gauge (blue.. flexible at low temps)
1 50 ft 12 gauge (yellow. quality cord with lighted end)
1 80 ft 12 gauge (pink... thermoplastic jacket, stiff, but OK in warm weather)
1 100 ft 12 gauge (yellow... Thermoplastic jacket, durable, it lay in the grass for a year providing power to the shop from the house)
1 100 ft 12 gauge (orange... thermoplastic, rarely used)
1 40 ft 12 gauge (green... thermoplastic jacket, never out of the package)
3 homemade 14 gauge cords.......... made from used Carol Super VuTron SJOOW 14/3 I got out of the scrap bins at work. All were longer, black with dirt and had pinched broken places in them. I made one 50 ft, one about 30ish ft and one 40ish foot. Soaked them in Tide (with the ends out of the water) and wiped them with a scrub pad, they looked nearly new. I used good quality ends on them (Pass & Seymour on one, Daniel Woodhead on one and Leviton on the other)
As already noted, 16 gauge have their uses. I can run my 4 amp or 6 amp battery charger on something, way away from an outlet, or use a couple to run the blower to blow the mower off over by the fence (don't want a mess up by the building)
Charles