Colour was so critical with Concorde that the Pepsi blue scheme had to be checked with and approved by the manufacturer, and it was required that the wings remained white to ensure fuel temperature didn’t rise too high from absorption of sunlight. Restrictions were placed on the blue aircraft by the manufacturers at speeds above Mach 1.7 - http://www.concordesst.com/history/events/pepsi.html
They did use paint, it was applied by the Air France paint shop at Paris Orly. I’m not sure Vinyl wrap would have been possible due to heat bubbling and the fact that the aircraft stretches by about 25cm at Mach 2.
Concorde is a bit of a special case. Skin friction is much less of an issue for most airliners. I’m not sure about weight being such an issue with white though. Depending on what you’re trying to paint, you can need more white to ensure good coverage than a darker colour, so even if it’s lighter gallon for gallon, you might not save anything. White is advantageous on commercial aircraft for all sorts of reasons. Heat reflection is a big one. Skin cracks and things like oil/hydraulic leaks are easier to spot. White is best for visibility for aircraft that have ditched on water. Multiple colours add weight if there are substantial areas of the secondary colours (you tend to paint the base colour and apply other colours over the top) so schemes that are chiefly one colour make more sense - and it makes most sense if the predominant colour is white.
The SR-71 is another special case. Its black paint contained microscopic iron balls to dissipate electromagnetic energy and according to some accounts, reduce radar returns. The SR-71 has a ‘heat sink’ structure unlike most aircraft, and is designed to allow heat to conduct from hot areas to cooler areas (and black is better at radiating heat). But for thermal protection, white is best. Another high flying supersonic military aircraft, the Tupolev Tu-160 is white overall.