あまり・あんまり is frequently found paired in negative verb clauses, which is where the "not too" part of the meaning comes from. 余り itself refers to a remainder value, of which as a modifier to 好き is how you get the notion of an amount of "liking something" with the negatively conjugated copular, basically defining that "amount of [liking something]" to be negative overall.
You will eventually see this negative construct again in the form of のあまり~ない. Japanese is an agglutinative language, which unlike English uses conjugations to more or less dictate the overall meaning of a clause.
The TL;DR is to pay extra attention to how the very conjugates in a sentence to get a hint as to how things like adverbs and other modifiers are altered in meaning. The patterns are common so if you pay more attention early, you'll come to feel them more intuitively sooner. >>142924009
Learn what the spoiler function is used for, you fucking sperg.