The Distant Spell metamagic option's first effect enables a sorcerer to double the range of a spell (that has a normal range of 5 feet or greater).
The counterspell spell has a listed range of 60 feet, but also has the following casting time (emphasis mine):
1 reaction, which you take when you see a creature within 60 feet of you casting a spell
Interestingly, it says "within 60 feet", instead of "within range".
If a sorcerer applied the Distant Spell metamagic to a counterspell in order to counter a spell that he sees being cast from somewhere between 60 and 120 feet of him, would the counterspell work?
The same logic goes for the feather fall spell, which also has a range of "60 feet"; its casting time is listed as "1 reaction, which you take when you or a creature within 60 feet of you falls".