This is Weinbaum's last year of eligibility as far as I know, since I'm pretty sure all his other posthumously-published works were published in years that had Hugo awards.
later - I'm an idiot - it's works appearing in 1938 that are eligible. Which means his only eligible stories are
"Revolution of 1950" 10-11/38 Amazing (with Roger Sherman Hoar writing as Ralph Milne Farley)
"Tidal Moon" in 12/38 Thrilling Wonder (with Helen Weinbaum, his sister)
Neither unfortunately his best work.