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.
Just an idea:
The first typewriter started at this time. When I check the German Wikipedia for Schreibmaschine, the first German typewriter was produced 1882/83.
Perhaps they used typewriter without
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":
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.