In calculating policy gradients, wouldn't longer trajectories have more weight according to the policy gradient formula?
wouldn't longer trajectories get more weight?


Not necessarily. Gradient $\triangledown_{\theta}$ could be negative or positive (1D analogy), therefore, larger number of gradients could have a smaller weight, which makes sense. A consistent short trajectory is more informative (has more weight) than an inconsistent long trajectory with sign-alternating policy gradients.


  Why would it work like that?


If we are comparing two consistent trajectories, where most gradients are in the same direction, this formula makes sense again. A long consistent trajectory contains more useful information (more steps that confirm each other) than a short one. In real life, compare the informativeness of a successful week to a successful year for your policy learning.