As far as your silly experiment, your problem arises in that ly is used to convert an adjective into an adverb, with the definition "in a [adjective] manner".
Thus, sillily is a word ("in a silly manner")
As far as "in a sillier manner", there are two rules for forming a superlative from an adverb. If the adverb was formed by adding ly to an adjective, you must use most or more.
"In a sillier manner" -> more sillily
"In the silliest manner" -> most sillily
If an adverb is the same as the adjective form, you can make a superlative using er or est
"In a faster manner" -> faster (ex. "He ran faster")
"In the fastest manner" -> fastest (ex. "He ran fastest")
As for sillilily, this is entirely nonsense. The reason is that our ly rule only applies to adjectives. You can not apply ly to an adverb and expect a "double adverb". An attempt to apply the rule directly would result in:
"In a sillily manner"
Notice that since manner is a noun, it should not have an adverb describing it. In your examples the word "suggesting" came out of nowhere. Nothing in the grammatical construction implied that there was suggestion.
In the case of sillililiest we encounter both of the above problems simultaneously. First, you attempted to make an adverb from an adverb by adding ly
sillily -> sillilily
Then you attempted to apply est or er to make a superlative
sillilily -> sillililiest
Both of these can not be done. The first because ly only applies to adjectives, not adverbs. The second because to make a superlative from an adverb which was formed by adding ly, you must use 'more' or 'most'. Again- you introduced the word "suggesting" which came out of nowhere.
Both are grammatical, but they mean different things.
The first supposes that several days this month have been warmer than the others, and that today is one of them. For example, the temperatures on 2, 8 and 19 September have been 16, 14 and 23 degrees and the temperature today is 18 degrees. All the other days in the month have been cooler.
The second supposes that several days this month have been the warmest this month, and that, again, today is one of them. For this to be true, the temperature today and several other days must all have been, for example, 20 degrees, when the temperature on all other days has been lower.
Best Answer
How many quarterbacks are there? If there is one quarterback, he can throw far.
If there are two quarterbacks, one can throw farther than the other.
You need a comparison between three of a thing to use farthest (or biggest, tallest, smartest, etc.)
If everybody on the team is throwing the ball, then you'd be technically correct to say he threw the farthest (if he did).
The difference between farther and further is another matter.