No BS Q Analysis
TLDR: Weaving is slightly more damage at all levels with base stats, is worse after 360 AP and gets better the more AS and AD you have. In a game only weave autos if the enemy is immobile and if you don't already one shot with QQQ->AA.
As a consequence of various (faulty) discussions, here are the actual numbers of Locke's Q.
A prerequisite to determine the damage of one combo vs another is that both combos are of equal length. In the above example I show a trade of 5s with both QQQ->Autos and Q->Weave. It is important to note that weaving without additional AS is always worse than QQQ->Auto if that is the extent of the possible trade. Also note that if you don't cancel the first AA windup with you Q animation weaving is always strictly worse.
Refer to this pdf hosted on google drive for the calculations that back up the video.
In most actual applications QQQ->AA is both safer and faster burst dmg delivery which is why it should be preffered. In extended trades weaving can be preferrable. Testing with runes like PTA, HOB and Conq still necessary; I used Electrocute because it doesn't fudge the damage numbers.