Gravity & Bio-mechanics
The principal contributing factors to physical size of fauna is: gravity and bio-mechanics. According to Jonathan Payne, a paleobiologist at Stanford University who has done extensive research on how body size has evolved over the history of life.
If you took an animal and blew it up in size, mathematics of bio-mechanics dictates that the creature’s mass would increase cubically, or by a power of three. However, by the same ratio of size increase, the width of the creature’s body, and thus its bones and muscles, would increase only by a power of two. As the alien creature gets bigger it needs to dedicate more and more of its body mass to its bones to support itself.
On Earth, a big factor that has historically (over the length of life on Earth) driven animal size is the percentage of oxygen in the air. More oxygen lead to bigger fauna, less oxygen lead to smaller fauna. It isn't entirely clear if this is mostly due to animal respiration or mostly due to availability of food.
The Earth’s biggest terrestrial animals, elephants, for instance, can reach about 13 feet tall and weigh up to 7.5 tons. In the past, however, life got far larger: Dinosaurs like the Titanosaur weighed in at nearly 80 tons—10 times larger than the African elephants of today. The reason has to do with the fact that dinosaurs were reptiles. To maintain their higher body temperatures, warm-blooded mammals spend about 10 times more energy than
cold-blooded reptiles do on their metabolisms. This is energy that a mammal can’t devote to increasing its body size. Consequently, terrestrial mammals aren't very large in size.
Following from the previous point, aquatic fauna, the Blue Whale, is a mammal and larger than any terrestrial fauna ever. Of course buoyancy and gravity trade-off explain this disparity. An important distinction though is the foraging habit of Blue Whales. Blue whales swim across ranges of thousands of miles to find krill to eat. Even the African elephants can cover up to 80 miles in a day looking for vegetation. The large fauna require food to supply their metabolism, growth and reproduction requirements. An alien would need to move large distances to acquire all the food it needed unless the alien planet had surplus vegetation that somehow regrew quickly such that the gigantic alien did not need to cover thousands of miles on land to forage.
The largest animals through history on Earth are understandably herbivorous. Its a question of energy efficiency or economy of metabolism; how much metabolism is invested in acquisition of food? For comparison, consider carnivorous animals like lions and tigers on a hunt. They are physically strong animals but spend a lot of energy on hunting their prey. This energy could alternatively have been spent on growing bigger and reproduction, instead evolutionary forces drive these animals to work in groups (reproduction priority) rather than have larger individuals. On the other hand, herbivorous animals don't fight with their food, so physical strength beyond that required to support their own weight is not an evolutionary priority.
Speculative Gigantic Alien
Lets get our ingredient for gigantic alien
Foraging: Cornucopia of rapidly regenerating food source
Evolutionary pressure: Preference for physical size
A likely candidate alien would be a hybrid of flora and fauna. Unlike herbivorous animals that spend energy on eating plants that acquire and store energy from photosynthesis, the candidate alien has its own energy producing capability. This saves it time and energy on foraging.
The alien plant could have perennial incident solar energy, say there are multiple stars in the planetary system. Then this alien could be acquiring energy through some manner of photosynthetic process in a continuous manner.
This savings in metabolic energy could be spend on growth and building strength, which leads to gigantic and strong alien.
Answer: I AM GROOT
A flora-fauna hybrid alien.
Thanks to a comment, I did a bit more research on warm and cold blooded animals. I've mentioned some interesting points of distinction that would shed light on the kind of alien planet and alien creature. If we have full creative control then a synergy between planetary conditions and alien could be achieved.
Warm-blooded vs Cold-blooded metabolism and survival pros and cons:
There are many advantages to being warm-blooded. Warm-blooded animals can remain active in cold environments in which cold-blooded animals can hardly move. Warm-blooded animals can live in almost any surface environment on Earth, like in arctic regions or on high mountains where most cold-blooded animals would have difficulty surviving. Warm-blooded animals can remain active, seek food, and defend themselves in a wide range of outdoor temperatures. Cold-blooded animals can only do this when they are warm enough. A cold-blooded animal's level of activity depends upon the temperature of its surroundings. A reptile, for example, will increase its body temperature before hunting and is better able to escape predators when it is warm. Cold-blooded animals also need to be warm and active to find a mate and reproduce.
Being cold-blooded, however, has its advantages. Cold-blooded animals require much less energy to survive than warm-blooded animals do. Mammals and birds require much more food and energy than do cold-blooded animals of the same weight. This is because in warm-blooded animals, the heat loss from their bodies is proportional to the surface area of their bodies, while the heat created by their bodies is proportional to their mass. The ratio of a body's surface area to its mass is less the larger the animal is. This means that larger warm-blooded animals can generate more heat than they loose and more easily keep their body temperatures stable. Smaller warm-blooded animals loose heat more quickly. So, it is easier to stay warm by being larger. Warm-blooded animals cannot be too small or else they will loose heat faster than they can produce it.
Being large requires a greater food supply, but for mammals, being small also requires a lot of food to generate more heat. Small mammals need to eat very often to survive because they need more energy to keep a constant body temperature. They also need to eat high energy foods such as fruit, seed, and insects and even other small mammals. Larger mammals can get by with eating lower energy foods or eating less often. In an environment where food is scarce, such as in deserts, reptiles have an advantage. Since cold-blooded animals do not have to burn a lot of food to maintain a constant body temperature, they are more energy efficient and can survive longer periods without food. Many cold-blooded animals will try to keep their body temperatures as low as possible when food is scarce.
Another disadvantage to being warm-blooded is that warm-blooded bodies provide an nice warm environment for viruses, bacteria and parasites to live in. Mammals and birds tend to have more problems with these infections than do reptiles, whose constantly changing body temperatures make life more difficult for these invaders. However, an advantage of this is that mammals and birds have developed a stronger immune system than cold-blooded animals. A reptile's immune system is more efficient when the animals is warmer, however, since bacteria probably grow more slowly in lower temperatures, reptiles sometimes lower their body temperatures when they have an infection.
Finally, I haven't considered the possibility of gigantic size for extremophiles, which are creatures that live in extreme conditions, like hyperthermophiles. If the alien planet was something like Venus, and these aliens could absorb the energy in the high temperature, high chemical environment, they could solve their metabolism needs and possibly grow very large.