Rav Hirsch in explaining Bereishis 1:1 explains the usage of Shamaim as he had developed it in Jeshurun vol. VIII pg. 274 as
the designation of the whole extra-terrestrial world. He then explains the usage in 1:8 as well. Thus, there are different levels called שָׁמַיִם based on what they are being separated from. This then means the highest of those levels.
The phrase שְׁמֵי שָׁמַיִם means the ultimate level of the separations that are called by the term שָׁמַיִם which is therefore above all the others. Since we regard the earth as the position at we we have our point of view, the heavens are above us and we are looking up toward each level. The furthest heaven is thus (to our eyes) the highest or loftiest.