Originating from the reflexive verb form *-tise, from the Old Latvian verb forming suffix *-ti (now -t) combined with the old reflexive pronoun *se. The current pronunciation is explained either by metathesis (-tise > -ties), or by the dropping of the final "e" and expansion of the "i" to "ie" (-tise > -tis > -ties).
In either case, the specifically reflexive nature of the suffix appears to have been forgotten, evidenced by the absence of a reflexive meaning in multiple modern verbs (E.g. vēlēt becoming vēlēties, with the original meaning (To wish, desire, want) having shifted to the latter. The present meaning of vēlēt (To vote, elect) being artificially added in the 1800s or 1900s).
While in other instances forming verbs with meanings unrelated to the reflexive (E.g. klausīt - to obey, comply. klausīties - to listen in, to hear).
-ties