I think you're asking more about 'etymology' than 'grammar'. 'Harass' comes to English through the French word 'harasser'. The French got the word from the German word 'hare' which was used to encourage hunting dogs to chase their prey. As for why we spell it the way we do, it would be better to ask a French speaker. English borrows many words from other languages, so we can't claim that we have 'rules' for spelling. We just have many patterns.

Double letters serve a function--usually to make a vowel short. Sometimes with the case of ss, it changes the sound of the 's' from a (z) sound to a (s) sound. When the s comes at the end of a word, it usually takes the sound of (z). Think of the words has, was, his, days, etc. Therefore, using the double ss ensures the sound will be (s). Think of the root word for harassment, harass. If the s were alone at the end, it would sound like haraz. These are just basic phonics rules that we are not taught explicitly in school.

The verb is to 'harass' The noun is simply the verb plus the suffix '-ment'. Why do you think that this is a problem?