Janet said:

Yesterday I watched the beds
and the most stunted bed (closest to the willow) doesn't get sun until
11am. Our sun sets around 8pm right now (up to 9 during the longest
days in June) so these plants do get 8 hours of sunlight. After 11 it
gets really really hot and doesn't cool off until evening.
I started to think that maybe the melons might shut down during the
hottest part of the day, and since they missed all of that morning
sun, that might be what's stunting them.

Morning shade/afternoon sun is always more of a stress than morning sun/
afternoon shade.

Also, could the roots of the
willow be sending something toxic?

I couldn't find any information fingering willows as allelopathic. *Any* tree
will compete greedily with a vegetable garden for water and nutrients
(*especially* water), so that competition, combined with the morning shade,
could explain what's stunting your melons.

Tree roots entering the veggie garden to steal water and nutrients are a
particular problem of mine...
--
Pat in Plymouth MI

Any technology distinguishable from magic is insufficiently advanced.
(attributed to Don Marti)