The KJV popularized the notion of "giants" in ancient Palestine. The best-known example is, of course, Goliath–although he's not called a "giant". Unbelievers cite this as an example of Biblical mythology. There are several issues to sort out:
1. Height is relative. To be taller or shorter than someone else is not a measure of absolute height. Due to dietary deficiencies, ancient people were generally shorter than their well-fed modern counterparts–or so I've read. What might be towering by ancient standards might be nothing extraordinary by modern standards.
In addition, I've read that "All the available evidence tends to show that the ancient Hebrews were short of stature, compared with the other races in Palestine, particularly the Amorites." http://www.jewishencyclopedia.com/articles/13993-stature
If that's accurate, then modern readers need to guard against an anachronistic interpretation of OT references to "giants", lest we use modern experience as the frame of reference.
2. To my knowledge, ancient people lack the technological precision to have absolute weights and measures. It wasn't standardized in a way we take for granted today.
3. In his chapter on "Medicine in the Old Testament World," Donald Wiseman discusses giantism, with special reference to Goliath. B. Palmer, ed. Medicine and the Bible (Paternoster, 1986), 23. In an endnote, he says: "Skeletons 3.2 m. tall have been found elsewhere in Syro-Palestine," ibid. 244n58. Unfortunately, he cites no references, so it's not possible to confirm his claim.
4. According to the MT, Goliath was about 9' 9" tall (assuming the conventional interpretation of a cubit). One question is whether that's realistic. Some scholars attribute his staggering height to gigantism. However, there are prima facie problems with that explanation:
i) From what I've read, gigantism results in physical disabilities. How could Goliath be a great warrior if his athletic ability was compromised by gigantism? Likewise, I presume there's an upper limit on the human musculoskeletal system. The fact that we're bipedal may impose stricter constraints.
ii) Perhaps this could be salvaged by saying he only appeared to be physically formidable. His invincible appearance was sufficient to scare off competition. His huge weapons were props. Still, he seemed to have a reputation that preceded him.
5. We should make allowance for the possibility that if people are shorter, then cubits are shorter. It's a circular relation. If a cubit is defined by the distance between the elbow and the fingertip, that varies. In general, shorter men have shorter arms and fingers. If ancient Jews were shorter, the cubit might be shorter.
6. Another complication is that Josephus, the LXX, and the DDS give a lower reading of about 6' 9''. There are different ways to explain the conflicting data. On the one hand, the MT reading might reflect a hyperbolic emendation to exaggerate his height, therefore making David's success all the more impressive. Maybe the Massoretes changed the text.
Conversely, the lower reading might reflect a pious emendation to make the figure more realistic. Perhaps some scribes changed the text to make the account more credible.
Given the diverse attestation of the lower figure, in three different sources, this may well be based on an independent textual tradition. So perhaps that preserves the authentic Hebrew reading.
7. To my knowledge, 6' 9" would be a towering stature by ancient standards. To take a comparison, Brock Lesnar is a mere 6' 3". Yet he's physically imposing, even by modern standards.
8. In addition to diet, climate can also affect height. According to Bergmann's rule, species are generally larger in cooler climates, and smaller in hotter climates. On the one hand, larger bodies produce more heat. On the other hand, larger bodies are more efficient at conserving heat because they have proportionately less surface area.
(Mind you, there are different strategies for heat loss. Take Allen's rule.)
Perhaps the tall inhabitants of ancient Palestine migrated from northern latitudes.