To the best of my knowledge, signal flows mostly at the outer circumference of a cable with the inner/core mostly unused (any cable/thickness). This is more pronounced the higher the frequency. Some manufacturers use hollow cores with conducturs wound around it to mitigate this.
I don't think you need thick cable (a milimeter is probably plenty enough for average home length hifi runs without exhibiting audible resistance) for good bass but the material used both for the conductor and insulation is important as is configuration. Imo, the most likely scenario, when using thinner cabling is that you loose high frequencies (treble) and the cable will/can be perceived as sounding smoother rather than bass light. That at least has been my experience contrary to the common belief that thin cables lack bass.
PVC is not an ideal insulator but silver plating (or pure silver conductors) are arguably the best conductors (silver has some of the highest conductivity and doesn't loose it when tarnished either) ... it certainly doesn't do any harm.
Perhaps this explaines why I like the afromentioned VdH CS122 Hybrid. It follows good practice both with conductors and insulation. The only trick missed is perhaps a hollow core (as per some QED's which, technically and probably materially, should rank as some of the best cables available. They also publish measurements for each of their cables). Configuration is spaced rather than twisted, which has both some benefits and downfalls.
I am not a cable expert and the above simply reflects my preferences and limited experience. I also remember the very capable PaulMiller quoting that he personally would stick with silver plated copper. He has conducted numerous tests/measurements into cabling.
So, to sum up, imho you should use a thinner cable if you find your current sound to bright rather than a thicker cable to make up for any perceived shortfall in bass.
As always with cables, they may be used as very subtle tone controls but that's all.