Gear whine is caused by error in the teeth pattern between the gears. This stacked mesh error causes different noises depending on which parts of the tooth profile are in error. Different gear sets have different errors, which is why a given transmission can whine in 3rd but not in 2nd. The best transmissions have "matched" errors such that the total error is close to zero for each gear path. (Ex: input shaft to main shaft: +0.02, main shaft to first gear:-0.01, first gear to output shaft:-0.01, total error:0.00)
Using a thicker oil helps mask the noises by buffering the gear contact patches, which helps "zero" the error.
This is, of course, assuming nothing is actually wrong with the transmission, like a bad bearing or burned bushing. This type of noise as I described will be present during the entire life of the transmission, although it will get worse with age as gear faces wear and the gaps increase.