When to use words quite, rather, pretty, fairly etc: degree of downtoning

Some of them have differences of strengths, for instance, if something were described as "pretty large" or "fairly large" I would interpret as less large than something described as "quite large" or "rather large".

"Rather" sometimes has a slight connotation of unexpected, so if something was somewhat larger than expected I would prefer to use "rather large" than the others.

These preferences may vary from region to region and even person to person though.

Ok, I will take a crack at this:

• quite is good for expressing mild suprise at the extent/size: "I was quite pleased by the reception I received there."

• rather is a more posh version of quite.

• pretty, on the other hand, is to express faint enthusiasm: "I had a pretty good time, I might go there again sometime."

• fairly is even a bit less enthusiastic than pretty.

Each can be used, more or less ironically, for the opposite effect, though.

One could grow weary of pointing out that English doesn't actually have many "rules", and that it would be better in most cases to call potential candidates for that term "strong tendencies", since they're often not universally applicable.

OP himself may be exceptionally consistent in using rather rather than quite large, but that's really just his preference. Though if this NGram means anything, it suggests average usage is tipping the other way. He's more in the mainstream with quite amazing, but this one backs up my own gut feeling that pretty soon pretty amazing will rule that particular roost.

In certain contexts, these kind of qualifiers can all have their own special nuances, but it would be a mistake to infer any consistent rule regarding which to use when. Nor is there any consistent hierarchy of "intensity" for rather, quite, pretty, very, etc. Many Brits, for example, would say that in some contexts, somewhat is far more intense than any of those. Any many (younger?) people use totally in ways that imply it's far less intense.

Strunk & White's rather delicious little subtlety:

Rather, very, little, pretty – these are the leeches that infest the pond of prose, sucking the blood of words. The constant use of the adjective little (except to indicate size) is particularly debilitating; we should all try to do a little better, we should all be very watchful of this rule, for it is a rather important one and we are all pretty sure to violate it now and then

As quoted in Harpers Bazaar, Diana described Charles as "pretty amazing".

This may not have been the Queen's English, but it was the Wife of the Heir Apparent's English, which is pretty authoritative.