I struggled with this as well (as we all did, I assume).
I found the curling was the worst when I packed them tightly, but I never put any type of weight on them because it felt odd to me to partially cut them off from airflow.
Do you move or remove the wood blanks (or whatever you are using) after a certain time?
Does it lead to issues if the wood brim on the drying rack is different in height to the thickness of the sticks?
I know what Dave described is commonly seen as the best and therefore most used method of drying, but I never actually tried it nor looked too deep into it, as I found a different solution that works for me.
I don't use these kind of drying racks that have the wooden brim, so there is no outer edge I can snug the sticks onto.
I found that spacing out the sticks, so there are no areas with significantly less air exposure helps a lot. For the first day, I usually cover them with a very thin cotton cloth. I dry them Either in my attic during the cold season or in a cellar-like room we store fire wood during warmer days. I try to find a place that is below max. 16°C; I found around 12°C to be ideal.
Spacing out the sticks while making sure they lay straight is a bit tedious and time intense. Definitely not something that works for someone doing this commercially. But for hobbyist small and micro-batches, it's quite ok.
I'd like to have an alternative method for the rare cases I make larger batches, though.
And to make me less dependent on seasons and temperature. (If it's too warm, I just don't make stick incense.)