Cebu Pacific is a Philippine low-cost airline , which has 6 A330 in its fleet. The capacity of each of them is 436 . As far as I know, one of the reasons why airlines introduce First Class cabins is because its impossible for them to fly with a huge number of passengers and their luggage. It makes the plane very heavy and less fuel efficient. That's why, we don't have any A380 with more than a capacity of 550 , against its maximum of 853. But, how does Cebu Pacific makes profits from operating a 436 seater A330( which commonly has a capacity of 300 people)?
First of all, keep in mind that the Philippines has one of the shortest average populations on Earth. Their average passenger weighs a lot less than an average American or European, since weight scales roughly with the cube of height. So, 436 Filipinos don't weigh nearly as much as 436, say, Americans or Europeans, assuming average populations from each group. According to Wikipedia, the average Filipino male of age >= 20 is only 5' 3.5" (162cm) and the average female age >= 20 is 4' 11" (150 cm.) Compare those numbers to 5' 9.5" (176 cm) for males and 5' 4" (162 cm) for females for Americans age >= 20. Considering the roughly cubic scale, that's a pretty significant mass difference.
Second, why would putting more passengers on board not be fuel efficient? It will make the aircraft heavier, but it also means that you're carrying that many more people in one trip. My guess would be that you'll burn less fuel per passenger-mile, rather than more. To get a rough estimate, an A330-300 has an operating empty weight of about 274,500 lb. and it can carry about 175,170 lb. of Jet-A. If we assume the average Filipino weighs about 120 lb. (this seems like a reasonable guess based on my experiences in the Philippines,) 436 passengers would come out to 52,320 lb. while the 293 passengers on Delta's A330-300 seat configuration would be 35,160 lb. So, you're increasing mass before fuel by only around 5.5% while increasing passenger count by a whooping 49%. It would be hard to find a scenario in which that does not use less fuel per passenger-mile (unless, of course, you're overweight and can't take off at all.)
Regarding the issue of avoiding being overweight (and, thus, being able to take off,) Cebu Pacific normally doesn't run routes anywhere near the 6,100 nmi range of a fully-loaded A330-300. This means that they won't need to carry a full fuel load. Even a 10% reduction in fuel load from the maximum capacity of an A330-300 would equal the entire added weight of going from 293 passengers to 436. Even at full fuel load, though, judging from the previously-referenced numbers on Wikipedia, we get:
Operating Empty Weight (OEW): 274,500 lb.
Full Fuel Load: 175,170 lb.
436 120 lb. passengers: 52,320 lb.
14 flight + cabin crew x 120 lb. = 1,680 lb.
Total before cargo: 503,670 lb.
Maximum Takeoff Weight (MTOW): 534,000 lb.
So, that still leaves 30,000 lb. for cargo and anything else that's needed, even if they did need to carry a full fuel load for some reason.
The issue of why Cebu Pacific doesn't offer Business/First class cabins was also mentioned. The reasons for this are mostly their target demographic and their route network (combined with the already-explained lack of weight limit.) While there are many business travelers going to and from Cebu City, the routes on which these travelers are typically traveling are already well-served by several high-end airlines that also offer onward connections to Europe and the Americas (e.g. Cathay Pacific to Hong Kong, Korean Air and Asiana to Seoul, Japan Airlines to Tokyo, Emirates to Dubai, EVA to Taipei.) Additionally, Philippine Airlines also already competes in that space (in addition to apparently offering direct flights from Cebu to LAX now, which I think is a rather recent development.)
With their low-cost model and lack of alliance partners for onward connections, it would be difficult for Cebu Pacific to compete for the already well-served premium-cabin demand in Cebu. Instead, their business model is catered to serving Filipinos traveling between islands and to regional destinations where lots of Filipinos work out-of-country. Last I heard, approximately 10,000,000 Filipinos worked outside the Philippines (around 10% of their total population,) so serving that demographic is not a small market. In case it's not obvious, this is an extremely price-sensitive demographic which is well-served by Cebu Pacific's low-cost model.
It should probably also be noted that, while 436 passengers on an A330 is unique to Cebu Pacific, high-density economy-only configurations in general aren't. Lots of regional-service low-cost carriers offer high-density economy-only fleets, even in less cost-sensitive areas like Europe, Canada, and the U.S. In Cebu Pacific's own region, AirAsia and Tigerair also operate similar high-density, economy-only fleets targeting the same demographic (though, admittedly, AirAsia X does have 2 rows of business-class seats in their A330s, but these are on longer routes than Cebu Pacific normally serves, e.g. Singapore-Australia.)
I don't know if the A330 runs into weight and balance problems with 436 passengers AND full fuel. It is very common, however, in small planes for the plane to be over max gross weight with all the seats full and also with tanks full. You have to restrict how many passengers you carry, or make intermediate stops for more fuel.
Since Cebu Pacific has many shorter leg lengths perhaps they can fill all the seats and still take on board needed fuel plus reserves and be below gross weight restrictions.
As you point out, adding business and first class seating reduces the overall weight of the passenger load. On a weight restricted flight, that alone will increase overall revenue.
While adding weight to an aeroplane increases fuel consumption because the wings have to work slightly harder and the nose has to be slightly higher which increases drag, and thus an higher power setting is required. So adding even one person is not fuel efficient compared to one less person. But the money received from that extra person will outweigh the additional fuel required.