Actually, you have it backwards. The "nominal" voltage for professional balanced lines is 1.23 VAC, or +4 dbu for "0" db (usually taken as being -20db of full scale digital). For full scale digital (full output for a digital signal) which is +20 db above this level, the voltage would be 9.75 VAC. So the voltage in a balanced line is significantly higher than in a consumer unbalanced line.

Professional balanced microphone lines run at very low voltages, but we're talking about line level here.

Single ended consumer lines usually run at an approximate nominal voltage of around .3 VAC (300 millivolts - it's not a hard and fast specification). At full scale digital for this type of cable, the voltage would be around 3 VAC. The standard output level for consumer CD players is 2 VAC for full scale digital, or .2 VAC (200 millivolts) for "nominal" level.

The size of the conductors in low level interconnects has no effect on signal transmission loss since the load impedances are always very high (over 10,000 ohms) and there is very, very little current flowing (thus no real voltage drop with long cables). In speaker cables, the impedances are much lower (8 ohms usually) and there is substantial current flowing, so the resistance of the cable must be very low. This means the cable must be very large so that long runs don't present significant resistance.

Line level cables can therefore be just about any gauge you want. Professional line level wiring in studios is usually 24 gauge, which is quite small.