Tiger Airways and Jetstar are two discount airlines which fly from Singapore to Hong Kong.
Getting back to the topic, these two airlines are affordable options to SIN as compared with CX or SG. Tiger is running flights as low at $478 and Jetstar $578, both before taxes and luggage fees. They do allow 7kg and 10 kg respectively, of carry-on luggage free. In HKG I haven’t had a problem bringing carry-on luggage that was heavier, though I have seen scales in SIN, so I’d be slightly more weary on the return.
As with all discount airlines in Asia, leg room is tight, and you’ll have to pay for any checked bags.
A sidenote, Tiger also flies to Clark near Manila in the Philippines for $229 before taxes.