There are many halachic chazakas. Most of them are halachic assumptions, such as:
Keeping things the way they always were - Either financial (Chezkas Marei Kama) or religious (Chezkas Tahara, Chezkas Tuma - that we assume that once something was in one state, it stays that way until we bring proof otherwise).
Interpersonal assumptions - e.g Chazaka She'ein Adam Meiz Panav (we assume a borrower won't lie completely to his lender), Milsa D'avida Le'Gluiya (people don't lie when their lie will be caught), etc.
What is the source of these Chazakas. Is it a Halacha LeMoshe MiSinai or is it a Sevara? If it is a Sevara, are any proofs brought that these Sevaras are true?
מנא הא מלתא דאמור רבנן אוקי מילתא אחזקיה? אמר רבי שמואל בר נחמני אמר ר' יונתן, אמר קרא: ויצא הכהן מן הבית אל פתח הבית והסגיר את הבית שבעת ימים, דלמא אדנפיק ואתא בצר ליה שיעורא! אלא לאו משום דאמרינן אוקי אחזקיה.
Whence do we know that which the Rabbis said, "establish it based on its previous status [Chazaka]"? Rabbi Shemuel bar Nachmeni said in the name of Rabbi Yochanan: It says in the verse (Leviticus 14:38): "Then the kohen shall go out of the house to the entrance of the house, and he shall quarantine the house for seven days." Perhaps once he leaves [the house] the size [of the Tzara'at patch] shrunk below the minimum size? Rather we must say that we can establish things based on their previous status [Chazaka].