Yes ,they tend to burn up..
The reason for the different gauge wires is b/c there is less amperage draw for low fan as the resistor is in series with the circuit, whereas the other wire by-passes the resistor for high fan, which has a higher draw.
Some guys do go back to the relay with a heavier wire because they were marginal to begin with..the trick is to have good , solid connections at the resistor ends..I use appliance wire end/connectors [ hardware store item..or RS] as they can withstand the heat much better..