We have ADCO on record saying that thin SS barrels aren't
acurate over a longer rd. count.- and looking at his bull barrels,
John Noveske seems to be of the same opinion.
So, once we rule out thick SS barrels due to weight concerns and conventional/
chrome lined barrels due to inaccuracy, what barrel material (& lining)
is left that offers both optimum accuracy and ruggedness in a thiner
Match stainless, polygonal profiled rifling, and carbon fiber wrap with Electroless nickle/Silicon carbide lining.
Match stainless polygonal will be very accurate. They have shown to maintain sub MOA for 14K rounds in the Noveske barrels as polygonal profiled rifling is less suceptable to throat errosion. Carbon fiber wrap allows 3X better cooling and cuts throat erosion in half thus doubling barrel life all on its own. Lighter than a light weight, still allows HBAR like accuracy and HBAR profile. Electroless nickle/silicon carbide lining can be applied to stainless unlike hard chrome, can be applied more evenly and thinner than hard chrome thus does not reduce accuracy. It has better adhesion than hard chrome, more wear resistant than hard chrome, cant get micro fractures to substrate metal like hard chrome, more corrosion resistant than hard chrome, less friction than hard chrome, can hold oil unlike hard chrome if you want that, etc.
You can buy such a barrel and lining from ABS barrels but it will be many hundreds of dollars. If I had to guess current prices I would say $750 for such a barrel in 5.56 but perhaps as low as $650 if they have not incurred the $100 price increase due to carbon fiber price jump. Mine should be ready in about 6 weeks.
Of course this barrel is not a thinner profile but I assumed you meant lightweight and not the actual thickness of the barrel steel. I hope this thing shoots as well as I anticipate. Expect a range report in a couple months.