Notice that the "hasst" form gained popularity towards the end of the 19th century, only to drop again in favor of "haßt" later on. I noticed the same pattern on other words using the ß. Why?
At that time the German language wasn't as regulated as it is today. Konrad Duden started to harmonize the German language around 1871. Before it was more "Wild West" than typical German "standard for everything".
The "s", "ß" and the long s ("ſ") were always part of these reforms. E.g. Duden had the opinion you should write like you speak (what would mean "ss" in hasst, because it is a "short" sound). But for the noun "Hass" it wasn't common to use "ss", because (I think) there was always a special "s" in German when standing at the end of a word.
So opinions differed and the reform from 1901 cleared some of these disputes (more or less). So my guess is that this popularity peak is due to the reforms and their disputes, which occurred around that time period.
In the "II. orthograhische Konferenz" held in 1901 it was decided to follow the rules of Adelung who wrote in his "Grammatisch-kritisches Wörterbuch der Hochdeutschen Mundart":
(bb) In der Mitte einer Sylbe, wenn nach dem ss ein e weggeworfen worden, oder wenn es doch aus dem ss entstanden ist; er ißt von isset, heißt, beißt, haßt, gleißt, gewußt, ich wußte.
This means in the example given that an 'ss' is written by 'ß' in case an 'e' was thrown away, as would be the case in "haßt" derived from "hasset".
By introducing this rule officially in 1901 we may explain why there is a decrease of 'ss', and an increase of 'ß' starting from this date. Favouring 'ss' earlier comes from the concurrent rule of Heyse that was officially introduced in the "I. Orthographische Konferenz" in 1876 and was reintroduced in the "Rechtschreibreform 1996".
Note: This rules may explain most variations in orthography of 'ss' vs. 'ß' however the example I gave in my comment above on "Straße" vs. "Strasse" does not fit. It may therefore be more than that.
Rise of ss tied to antiqua
During the course of the 19th century, German typesetting shifted more and more from blackletter to antiqua. This meant that the spelling ss became more and more common, since ß was one of the typical ligatures only used in blackletter typesetting.
The letter ß in antiqua was only invented at the very end of the 19th century and became standard with the 1902 spelling reform.
The Google ngram viewer is not trustworthy
The Google ngram viewer is a highly dubious source in this regard. We must suspect that it has a bias towards antiqua books. Google filtered out low quality scans, and scans of blackletter prints tend to have lower quality than scans of antiqua prints. Therefore, the ngram viewer probably shows a disproportionate number of antiqua prints, thus not representing how things really were.
In addition to that, there is relatively little data up until the mid 19th century, so the quality is low.