*wegh-

The core idea of the root was:

moving, going, transporting

This is still quite obvious in relatives like way, voyage or vehicle as well as the German der Weg (the way), weg (away) and bewegen (to move)

Here’s an incomplete list of English members of the family:

• the way, away, always (what you move on)
• convey (“transport to”)
• evict (“transport out”)
• vehicle (“transporter”)
• wiggle (move back and forth)
• via (from Latin “via”- way)
• voyage, envoy, convoy (also from Latin “via”)
• vector (from a Latin word for “carrier”)
• trivia, trivial (a place where 3 roads meet -> a common place)
• previous (“the way before”)
• obvious (“the way in front”)
• vogue (fluctuating, balancing oneself)
• wagon (transporting device)
• weigh, weight (shifted from transporting to bearing weight to just measuring it) 

The German preposition wegen becomes clear once you think of it as “by way of”, which also expresses causality in a way.