There are many ways in which sound can be recorded onto (and played back from) a DV cassette. It could be recorded as just Mono sound (probable, if it was copied from a 16mm film) which means that only half your stereo track has anything on it hence the low sound level. Some DVD players may compensate for this (when detecting mono sound) and may play back the same sound from both left and right channels thus giving reasonable sound.
The (possibly mono) sound may have been recorded onto the DV cassette as "12-bit" audio, instead of the higher-spec "16-bit" audio. [This allows an extra sound track to be recorded onto the tape afterwards.]
If it is mono - and you've got the sound on only one half of the two available stereo channels - then, if it's a 12-bit recording, you may have only one quarter of the available sound coming out, depending on how the 'mix' of the two available 12-bit tracks has been set up. (My Sony TRV900E, for instance, allows the balance to be swung way over to stereo track 1, or stereo track 2, or somewhere midway between them.)
I would listen to the sound via headphones as you replay it from the deck, to hear whether you've got mono or stereo sound, and whether it's coming out on one channel (e.g.; left) or both. That'll give a clue as to what's on the tape. Also check the deck's output settings: what kind of audio is it reading stereo track 1, stereo track 2 or a mixture?
Does the deck show - on a monitor - whether the cassette's audio is 12-bit (32KHz) or 16-bit (48KHz)?
The problem may be that your deck's analogue audio output (and the TV and the DVD player) is giving you one mono track out of both channels (left & right), but the digital delivery into iMovie is providing that same mono signal into only one half of a pair of stereo channels. If so, the solution would be to use some software (e.g.; Sound Studio which may have been bundled with your Mac look in 'Applications') to 'pan' (or to 'center') the audio to midway between stereo left & right, or to copy the, say, left channel to the right channel but if that's slightly out-of-sync you'll get horrible out-of-phase 'drainpipe' noises.