Somehow Hebrew made it to 1888 without a word for "serious." So it was up to Eliezer Ben Yehuda, reviver of the Hebrew language, to come up with one. He coined the word "re-tzi-NI," which in English can actually be translated quite a few ways, depending on context.
For instance, he first introduced the word to the world in an article he ran in his newspaper HaZvi, discussing the preparations for Purim – a holiday characterized by merrymaking and jesting: “And also the grand, the important, the retzini'im, who aren’t disposed to youthful actions, are strongly drawn by the general merriment; they can't help it.”
Retzini'im is the plural form of retzini, which Ben Yehuda described to his readers thusly: “In Arabic, dignified, one who doesn’t act lightly, serieux in French.”
What Ben Yehuda had done was take the Arabic word razin and create a Hebrew word, retzini, to mean "serious."
Though the usual word for "serious" in contemporary Arabic is jiddiy, the Arabic word razin is indeed closely related, but is generally translated as "demure.” It is etymologically related to “weighty” and is oddly fitting for serious, since Israelis often call an overly serious person kaved, which literally means "heavy." This is not a compliment.
The English word "serious" itself also comes from "heavy," though the path is a bit longer. It begins with the Old French word serioux, which itself derived from the Latin serus, all of which mean serious. The Latin word originated with a Proto-Indo-European word, swer, which means heavy. It seems that seriousness is intrinsically related to mass.
That said, the Hebrew root r-tz-n, has another meaning predating Ben Yehuda’s neologism, which in my opinion is more fitting to seriousness than brute weight. It is "will," as in "having a purpose and striving for it."
The word "earnest" (in the sense of serious, like in the title of the play "The Importance of Being Earnest") is etymologically related to this concept, originally coming – through Proto-Germanic – from the Proto-Indo-European word er, which meant to cause to move.