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
Weird. Here's a typical usage chart for XXXer / XXXest of the two with heavier/heaviest...
The same general pattern shows with older/oldest, larger/largest, etc. At some point in early C19, the superlative -est form starts to fall out of favour. Although it doesn't sound terrible to my modern ear, apparently these days we don't normally say something is the tallest of the two. The Google Books estimate in that link is totally unrealistic (there are only 27 instances, mostly old) but I'm prepared to believe there really are 44,000 instances of is the taller of the two as claimed.
What strikes me as particularly odd is that "irregular" worse/worst barely shows the effect...
I don't know why that change occurred a couple of centuries ago, but I consider it significant that worse/worst has been least affected, and better/best (also considered an irregular adjective) changed later than the strictly regular forms. My guess is that people who were less "schooled" (in logic, grammar, etc.) simply didn't bother making a special case for this particular comparative with only two candidates. Until education became more widespread, with more teachers telling more pupils to be more logical, and use the "right" word in such contexts.
But the reality is we don't apply this logic consistently. I suspect worse/worst is more resistant because it's not so obviously the pattern teachers (or our own "inner logician") rail against. But consider a context where the "only two candidates" aspect is less overt...
I know the dialogue's a bit crummy, but I certainly don't think changing it to richer would help.
TL;DR: It's just "grammatical logic" telling us not to use superlatives where comparatives would suffice. But we don't tend to do this so often unless the actual words (as opposed to the semantics or "overall utterance context", for example) make it glaringly obvious.