There are gusts coming down a reach. Do I sail a straight line at the mark, or weave with the gusts?

Weave. We sailed it both ways in a simulator with two identical boats on the same reach, same wind, same gust. Red sails dead straight at her mark, so the gust slides across her and is gone. Blue heads up to meet the gust, gets into it first, then bears away and rides it down the course, staying in the extra wind for nearly four seconds longer. When it leaves her she turns up, back toward her mark. She arrives more than a boat length ahead, even though she sailed about half a length further: in a gust, the extra speed is worth more than the extra distance. In a breeze, bearing away also keeps the boat flat so it can plane. Look upwind and you will see the gusts coming as dark patches on the water.

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<iframe width="560" height="315" src="https://www.youtube.com/embed/AdMI8vPuygg" title="Sailing Kiwi" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
<p><a href="https://sailing.kiwi.nz/v/AdMI8vPuygg/">Source: Sailing Kiwi</a></p>

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Next on this shelf — The Upwind Beat