Unable to prove at this time and thus will be mostly speculation, due to lack of source material from either author on this subject. I speculate coincidence.
Firstly, Mr. Martin has stated the he read Robert E. Howard, J.R.R. Tolkien, Robert A. Heinlein, Eric Frank Russell, and Andre Norton "pretty much interchangeably" and that he has always loved science fiction, horror, and fantasy and moved between them "pretty freely." So while George was influenced by Sci-Fi works, they are more the classical ones, not ones from the late 80s early 90s.
Next, the phonetic similarity between Weir and the German word Wehr are about exact. In German, Wehr is a word that means "defense" or is often used to refer to the particular defenses of a village or town, such as a trench or a wall. As such, a werhwood would be a group of trees that defend a people, which seems almost too coincidental to not be intentional in the case of Martin's novels. There are no George R.R. Martin sources located to back this speculation at this time.
As for Hyperion, I can find no reason for weirwood as a name for trees used to create support ribs on a treeship, or various expensive funitures. Though the name itself does sound good and fitting for a non-Earth tree, which is all that the author really needed in his novel.
In either case the word is certainly a neologism, and it is entirely possible for 2 separate authors to independently develop their own identical one. However, Martin would certainly be responsible for the common usage of this word, and not Simmon.