You're comparing a light, subsonic interceptor with no search radar and primitive missile capabilities (only available on the last versions) to a relatively modern multi-role fighter.
F-16 first flight was 45 years ago. Or put other way, F-16 first flight was significantly closer to MiG-17 first flight than F-35 (which gets to represent modern aircraft) first flight (24 years vs 32 years)
And F-16 was explicitly designed to pretty light-weight aircraft for its time, compared to e.g. its contemporary F-15:
> Boyd's design called for a light-weight fighter with a high thrust-to-weight ratio, high maneuverability, and a gross weight of less than 20,000 lb (9,100 kg), half that of its counterpart, the McDonnell Douglas F-15 Eagle
I think that using fourth and fifth generation to describe aircraft is better, especially when you combine it with production status.
For example, both the SU-27 and F-16 are clearly fourth generation, and both currently in production. Same with the F-15. They may have origins that are quite a long time ago, but they're still effective aircraft in many scenarios.
Fifth generation would be F-22, F-35, J-20, FC-31, and if you want to be generous, the Su-57. Stealth is the primary attribute, though supercruise is sometimes considered a key attribute as well.
I wouldn't argue for or against the use of the term "modern" to describe the F-16 since that's the most boring thing ever, but it is the most common fighter in service today, with multiple active production lines.
The empty weight is 8640 lb (3919 kg) and the maximum takeoff weight is 13375 lb (6069 kg).
It's maximum takeoff weight is still well below the empty weight (18,900 lbs) of an F-16.