I was doing a word study on הַשָּׁמַיִם in Gen 1:1 when I came across some references which says that it is a plural noun (since the suffix is plural), but some references say that it is a dual noun. Can I be enlightened about what is the actual number of הַשָּׁמַיִם and why?
The (masculine) dual ending is ־ַ֫יִם -ayim (with stress on the patakh) while the plural ending is ־ִים -îm. See §91b;90b of the grammar of Joüon and Muraoka. (Note that this means that the analysis depends on the vocalization and is not visible in the consonantal text.) Thus, this would suggest a dual for שָׁמַ֫יִם.
However, the root is שׁמי šmy, with a final yod. The plural would be שָׁמַיִים šāmayîm. This, due to phonological rules (which I do not fully understand myself), became שָׁמַ֫יִם šāmayim. Which is exactly the dual ending. Thus, this word is an apparent dual, but actually a plural form. For discussion and comparable instances of this sound change in Aramaic and Arabic, see §91f of Joüon-Muraoka.
The word is used in the plural because in the common Ancient Near Eastern worldview, there are three separate layers of heaven. Mesopotamian Cosmic Geography by Wayne Horowitz (2011, Eisenbrauns) provides a good overview of the topic.
In Hebrew, the "ayim" (patach-yod-hiriq-mem) ending is characteristic of dual masculine nouns, where as (hiriq-yod-mem) is characteristic of plural masculine nouns. Note that הַשָּׁמַיִם ends in patach-yod-hiriq-mem. You said that the "suffix is plural," but the suffix is actually dual.
Of course, without the Masoretic vowel points, the suffixes would look exactly the same.
Of course, just because הַשָּׁמַיִם is grammatically dual doesn't necessarily imply that two heavens are being referred to. Just like the word σαββατον (sabbath) often appears in the NT in the grammatical plural while still having a singular meaning (as in Matthew 28:1 and elsewhere). And in English, we say "a pair of pants."