Does a bipedal synthesist need the Weapon Training evolution to use weapons? Or (since they use the Summoner's feats) can they use whatever weapons they were proficient in?
Synthesist's weapon proficiencies are used.
The official site says that "The synthesist wears the eidolon like translucent, living armor. The eidolon mimics all of the synthesist’s movements, and the synthesist perceives through the eidolon’s senses and speaks through its voice, as the two are now one creature." and so on and then "While fused with his eidolon, the synthesist can use all of his own abilities and gear, except for his armor". I think that pretty much answers the question.