It costs airlines to interline bags and there is an industry trend to do it less and less. However, regardless what the rules are, when traveling in international F on a carrier like SQ or CX, what makes or breaks the interline bag check process is the attitude of the agent that checks you in at your point of origin.

In the dedicated First Class checkin line, the agents do not like to create issues-they are trained to treat their F passengers like gold, and they will frequently ignore the rules-checking an extra bag, not charging you if you are a few pounds over, and yes, interlining an extra and/or overweight bag on another carrier when the rules prohibit it. And generally, once the bags have been tagged, it is easier for the agent or baggage handler in the recheck area to just send it through without taking the time to find out whether it is "legal" and if not legal, what the charges should be.