As good a place as any to look would be FAR-23, which says:-
Sec. 23.3 Airplane categories.
(a) The normal category is limited to airplanes that have a seating
configuration, excluding pilot seats, of nine or less, a maximum
certificated takeoff weight of 12,500 pounds or less, and intended for
nonacrobatic operation. Nonacrobatic operation includes:
(1) Any maneuver incident to normal flying;
(2) Stalls (except whip stalls); and
(3) Lazy eights, chandelles, and steep turns, in which the angle of
bank is not more than 60 degrees.
(b) The utility category is limited to airplanes that have a seating
configuration, excluding pilot seats, of nine or less, a maximum
certificated takeoff weight of 12,500 pounds or less, and intended for
limited acrobatic operation. Airplanes certificated in the utility
category may be used in any of the operations covered under paragraph
(a) of this section and in limited acrobatic operations. Limited
acrobatic operation includes:
(1) Spins (if approved for the particular type of airplane); and
(2) Lazy eights, chandelles, and steep turns, or similar maneuvers,
in which the angle of bank is more than 60 degrees but not more than 90
degrees.
(c) The acrobatic category is limited to airplanes that have a
seating configuration, excluding pilot seats, of nine or less, a maximum
certificated takeoff weight of 12,500 pounds or less, and intended for
use without restrictions, other than those shown to be necessary as a
result of required flight tests.
(d) The commuter category is limited to propeller-driven,
multiengine airplanes that have a seating configuration, excluding pilot
seats, of 19 or less, and a maximum certificated takeoff weight of
19,000 pounds or less. The commuter category operation is limited to any
maneuver incident to normal flying, stalls (except whip stalls), and
steep turns, in which the angle of bank is not more than 60 degrees.
(e) Except for commuter category, airplanes may be type certificated
in more than one category if the requirements of each requested category
are met.
12,500lb = 5,670 kg, which is the actual figure but it regularly gets rounded informally to 5,700kg.
The actual value is fairly arbitrary, it was the point at which some committee back in the 1950s decided to separate "light" from "large" aeroplanes when they were drafting in the USA FAR-23 and FAR-25, and in Britain BCAR Section K and BCAR Section D. I guess that this was down to a survey of the current and projected aircraft types at that time.
CS.23, the European standard words it slightly differently:
CS 23.1 Applicability
(a) This airworthiness code is applicable to –
(1) Aeroplanes in the normal, utility
and aerobatic categories that have a seating
configuration, excluding the pilot seat(s), of
nine or fewer and a maximum certificated takeoff
weight of 5670 kg (12 500 lb) or less; and
(2) Propellerdriven
twinengined
aeroplanes in the commuter category that have a
seating configuration, excluding the pilot
seat(s), of nineteen or fewer and a maximum
certificated takeoff
weight of 8618 kg (19 000
lb) or less
But basically says the same thing.
Do note that for some piston-twins the figure isn't 5,670kg, it's 8,618kg.
G