rhetoric - Word for rhetorical style where different arguments get progressively weaker

Robusto gave a dailytrope.com link that defines catacosmesis as

Ordering words from greatest to least in dignity, or in correct order of time.

That definition appears to be copied from rhetoric.byu.edu. Somewhat more useful information is given by Henry Peachum, in the Schemas section of his 1593 book The Garden of Eloquence:

Catacosmesis, in Latine ordo, is a meete placing of words among themselves, wherof there be two kinds, the one when the worthiest word is set first, which order is naturall, as when we say: God and man, men and women, Sun and moone, life and death. And also when that is first told that was first done, which is necessary and seemly. ...
The use of this first kind of order, doth most properly serve to the propertie and elegancy of speech, and due observation of nature and dignitie: which forme is well represented in the civil and solemne customs of nations, where the worthiest person are alwaies first named and highest [placed].
The grace and comelinesse of this order is often diminished, and much blemished through want of discretion, or by rashnesse of the speaker, putting the lesse worthie, before the more worthy, ...

In short, the rhetorical form catacosmesis consists of placing words in proper order (when that proper order is most important first, or highest ranking first) to strengthen a passage. Catacosmesis is a positive term. Listing the best reasons first appears to be an example of catacosmesis. (As FumbleFingers points out, either arranging arguments to rise to a climax, or to fall from one in anticlimax, is rhetorically more effective than a pyramidal arrangement.)

One also finds the technique described as a “Arson, Murder, And Jaywalking” trope. TVtropes offers numerous examples, including:

• Juvenal (second century A.D.) uses this now and then in his satires. Most of the time his examples actually escalate (adultery, murder, murder of close relations) but now and then he throws in this trope, as in listing the dangers of living in Rome as “conflagrations, collapsing buildings, poets reciting in the month of August”.
• In her non-fiction book, Stiff: The Curious Lives of Human Cadavers, Mary Roach describes her experience at a mortuary college embalming lab. Anyone who enters the blood splash area has to wear plastic and latex to protect against HIV, hepatitis, and stains on your shirt.