The only free and comprehensive online etymological dictionary of the Spanish language
vacación f. (Noun) "vacation"

Very late 15th cent. From Latin vacationem, accusative of vacatio 'id.' From vacare "to be free from duties," "to be empty" (see vacar).
vacar (Verb) "to temporarily cease one's business or studies;" "to be empty;" (of a store or object) "to be with its owner absent"

From Latin vacare "to be free from duties;" "to be empty." Originally an adjective in Proto-Italic *wako- "empty." From Proto-Indo-European *h1u̯h2-ko- 'id.'

Romance: Western Vulgar Latin: Portuguese vagar, vacar, French vaquer, Italian vacare

Italic: Latin vastus "empty"

Indo-European: Celtic: Old Irish fás "empty;" Germanic: Gothic "," Old Norse "," Old High German wuosti "empty," Old Saxon wōsti 'id.,' Old English wōsti 'id.' (English waste)
vadear (Verb) "to wade"

Late 15th cent. From Latin vadum "ford," and not directly from vadere "to wade." See vado.
vado m. (Noun) "ford"

10th cent. From Latin vadum "ford." From Proto-Italic *waþo- 'id.' From Proto-Indo-European *u̯h2dh-o- 'id.'

Romance: Western Vulgar Latin: Portuguese vau, French gué, Italian guado; Eastern Vulgar Latin: Romanian vad; Sardinian: badu

Indo-European: Celtic: Welsh go-di-wawd "overtook;" Germanic: Old Norse vað "to wade," Old High German watan 'id.,' Old English wadan 'id.' (English to wade)
valer (Verb) "to help;" "to value," "to be worth"

Very late 11th cent. From Latin valere "to be well," "to be strong" From Proto-Italic *wal-ē- 'id.' From Proto-Indo-European *h2u̯lh1-eh1- "to be strong." Perhaps the root *h2u̯lh1- meant "to be big," "to be great."

Use of vale "okay" common in Spain. An innovation deriving from the sense of being "well."

Romance: Western Vulgar Latin: Asturian valer, Portuguese valer, Galician valer, Catalan valer, French valoir, Italian valere; Sardinian: balere

Italic: Oscan ϝαλε (wale) "farewell," Marrucinian uali 'id.,' Paelignian ual 'id.,' South Picene velaimes "of the best"

Indo-European: Celtic: Old Irish fallnaithir "to rule;" Germanic: Gothic waldan "to rule," Old Norse valda 'id.,' Old High German walten 'id.,' Old English wealdan "to wield power" (English to wield); Balto-Slavic: Chuch Slavic vladěti "to rule," Russian vladét' "to own," Polish wɫadać "to rule," Slovene vládati 'id.,' Old Prussian weldīsnan "inheritance," Lithuanian veldė́ti "to inherit," Latvian vàldît "to rule;" Tocharian: A wäl "king," B walo 'id.;' Anatolian: Hittite hulle-zi "to defeat"
válido (Adjective) "valid"

17th cent. From Latin validus "valid," but originally "strong," "healthy;" from the verb valere "to be healthy" (see valer).

Romance: Western Vulgar Latin: Asturian válidu, Portuguese válido, Catalan vàlid, French valide, Italian valido; Eastern Vulgar Latin: Romanian valid
valido (Noun, Adjective) "favorite"

17th cent. From the past participle of valer.

Romance: Western Vulgar Latin: Asturian valer, Portuguese valer, Galician valer, Catalan valer, French valoir, Italian valere; Sardinian: balere, baliri, valere
valiente (Adjective, Noun) "valient;" "valient person"

10th cent. meaning of "worthy;" the modern sense of valor is from the 12th cent. An adjectival from Latin valentem, accusative of valens 'id.' From valere "to be strong" (see valer).

Romance: Western Vulgar Latin: Portuguese valete, Catalan valent, French vaillant, Italian valente
valor m. (Noun) "value;" "courage"

12th cent. From Latin valorem, accusative of valor "value." From valere "to be strong" (see valer).

Romance: Western Vulgar Latin: Asturian valor, Portuguese valor, Galician valor, Catalan valor, French valeur, Italian valore; Eastern Vulgar Latin: Romania valoare; Sardinian: balore
vario (Adjective) "various"

15th cent. From Latin varius 'id.' Of unknown origin.

Romance: Western Vulgar Latin: Portuguese vário, Galician veiro, French vair, Italian vaio; Eastern Vulgar Latin: Romanian vare

Italic: Latin vafer? "clever" (a connection is formally possible)