From my reading of the rules, this is acceptable, but I thought I'd throw it out there:
After the first game of a match at FNM, I am allowed to add cards to my deck from my sideboard, even if I don't take any out. So, if I played game 1 with a 60-card deck and 15-card sideboard, I am allowed to play game 2 with a 63-card deck, leaving only 12 cards in my sideboard.
From my reading of the rules, this is acceptable, but I thought I'd throw it out there:
After the first game of a match at FNM, I am allowed to add cards to my deck from my sideboard, even if I don't take any out. So, if I played game 1 with a 60-card deck and 15-card sideboard, I am allowed to play game 2 with a 63-card deck, leaving only 12 cards in my sideboard.
Your sideboard and deck have to be legal at all times. This means at least 60 cards in deck and at most 15 cards in SB. So what you describe is legal. Note that this is a relatively new rule which was introduced somewhere around Magic 2014. Used to be 60+ cards in deck, exactly 15 in SB, and mandatory 1-for-1 swap.
In general, both under the comprehensive rules and under the Magic Tournament Rules, you may have more than sixty cards in your deck, whether in constructed or limited play (C.R. 100.2a-b, 100.5; M.T.R. 6.1, 7.1), but not fewer than sixty in constructed play or forty in limited play (C.R. 100.2a-b; M.T.R. 6.1, 7.1), and you may have "no more than fifteen cards", so even none, in your sideboard in constructed play (C.R. 100.4a; M.T.R. 6.1). (However, the Commander variant and the Brawl option have a maximum deck size [C.R. 100.5, 903.5a, 903.12d].) Note that C.R. 100.4 says a player "may ... have a sideboard", and both that rule and M.T.R. 3.16 speak of "modify[ing] [the player's] deck", not necessarily of exchanging cards one-for-one between the deck and sideboard.
To clarify one point: Under M.T.R. 3.16, "[t]he deck and sideboard must each be returned to their original compositions before the first game of each match" in most sanctioned tournaments, except in certain Limited format tournaments (M.T.R. 7.3) (for its part, C.R. 100.4 speaks only of using a sideboard to modify a deck "between games of a match").
EDIT (Apr. 25): Some sideboard rules were moved in the Amonkhet version of the Magic Tournament Rules.
EDIT (Sep. 21, 2019): Update quoted text.
EDIT (Apr. 17, 2020): Edited to conform to rule change with Ikoria: Lair of Behemoths.
EDIT (Jul. 13, 2022): Add rule citation.
EDIT (Nov. 4, 2022): Edit rule citations.
After the first game of a match at FNM, I am allowed to add cards to my deck from my sideboard, even if I don't take any out. So, if I played game 1 with a 60-card deck and 15-card sideboard, I am allowed to play game 2 with a 63-card deck, leaving only 12 cards in my sideboard.
Your sideboard and deck have to be legal at all times. This means at least 60 cards in deck and at most 15 cards in SB. So what you describe is legal. Note that this is a relatively new rule which was introduced somewhere around Magic 2014. Used to be 60+ cards in deck, exactly 15 in SB, and mandatory 1-for-1 swap.
To clarify one point: Under M.T.R. 3.16, "[t]he deck and sideboard must each be returned to their original compositions before the first game of each match" in most sanctioned tournaments, except in certain Limited format tournaments (M.T.R. 7.3) (for its part, C.R. 100.4 speaks only of using a sideboard to modify a deck "between games of a match").
EDIT (Apr. 25): Some sideboard rules were moved in the Amonkhet version of the Magic Tournament Rules.
EDIT (Sep. 21, 2019): Update quoted text.
EDIT (Apr. 17, 2020): Edited to conform to rule change with Ikoria: Lair of Behemoths.
EDIT (Jul. 13, 2022): Add rule citation.
EDIT (Nov. 4, 2022): Edit rule citations.