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His trebuchet launched a 4 gram projectile at 776 miles per hour.

That's obviously extremely lightweight for trebuchet payload, but for comparison, his projectile is approximately 62 grains so approximately twice as heavy as 30 grain high speed 22LR rounds. And approximately 1.5 times as heavy as 40 grain subsonic rounds.

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What does grains mean in this context?

It’s a super old unit of measurement for mass [0], idea being that a “grain” is a single seed of wheat etc.

1 gram is a little over 15 grains, and there are 7000 grains per (avoirdupois) pound.

0: https://en.wikipedia.org/wiki/Grain_(unit)

It's a unit of mass used in the firearms world

325 mg aspirin pills were originally 5 grains. A carat was 4 grains. The unit was used by apothecaries, jewelers, and bullet makers.

another way for america to avoid the metric system at all costs