Somewhat disputed. There are two main competing hypotheses:
* Usually held to derive via Proto-Italic *swerjos from Proto-Indo-European *swer-yo-s, from the root *swer- (“heavy”). Cognate with Old English swǣr (“heavy, grave, grievous”), German schwer (“hard, difficult, heavy”), Lithuanian sverti (“to weigh, balance”), svarùs (“heavy”). More at sweer.
* According to De Vaan, rather from Proto-Italic *sērjos, from Proto-Indo-European *seh₁-ro-s + *-yo-, from an uncertain root *seh₁- (“to go slowly?”) (cf. sēgnis (“slow, tardy, sluggish, lazy”)). In this case, equivalent to sērus (“slow, tardy”) + -ius, with semantic shift "slow" > "tiring" > "heavy" > "grave, serious".