This question seems very similar to an earlier question, differing mainly in the earlier question asking why earlier species were giant (or why such is less common now). (The answers to the earlier mostly addressed the content of the later question and not the specific historical factors.)
A comment to the earlier question asked for a clarification: Do you mean "what was the reason for some plant and animals to become giant in course of evolution?" or probably "What are the advances and drawbacks of being a giant plant or animal organism?" Even under natural selection these are distinct questions--the former might include "accidental" causes of size differences which are selection neutral (e.g., a particular gene might have a beneficial effect and a selection-neutral [or less negative than the other benefit] size effect) and the former seems to emphasize environment factors or perhaps specific historical factors (but the historical factors probably differed, e.g., huge dragonflies might have been more practical with higher oxygen concentration and/or a denser atmosphere but such factors might be insignificant in explaining dinosaur or Giant Sloth sizes); however, they are similar (and the answers--mostly avoiding the historical factors--are even more likely to be similar).
Anyway, what are the guidelines for judging a question to be a duplicate?