Why do onsets not count for syllable weight in phonological processes?

Question

Whether a syllable has a heavy or light rime is often important in whether it will participate in phonological processes, and whether it will receive stress. For example, in Latin, stress is on the penult if it is long in traditional terminology, i.e. heavy (CVV or CVC), otherwise it is on the on the antepenult:

Ca.'tul.lus (the poet) vs. 'ca.tu.lus (young animal)

Of course, languages differ as to whether they treat all types of heavy syllables the same, distinguish between heavy and superheavy syllables, treat geminates the same as other heavy syllables, etc. But is there any good (theoretical) reason why the onset should not count? Does any language treat syllables differently (in some way) depending on whether they have an onset or not, or a simple onset versus a complex onset?

Answer 1

Found an example of a language in which onsets matter for stress placement. It's Piraha (of course).

Apparently the syllables are subject to a prominence system, whereby long vowels>short vowels, and among syllables of the same vowel length, voiceless onset>voiced onset>onsetless. (There are no onsetless short syllables.)

The full prominence system would be: (T=any voiceless consonant; D=any voiced consonant)

TVV > DVV > VV > TV > DV (> V)

Stress is assigned to one of the last three syllables in a word, according to prominence. In cases of equal prominence, the rightmost syllable wins. I give a few examples below, with stress indicated by boldface type (tonal distinctions not marked).

1) bi gi 'earth'
2) pao hoa hai 'anaconda'
3) baa gi so 'many'
4) ʔi poi hi 'woman'
5) ho ao ba 'give'
6) ʔa ba gi 'toucan'
7) pii gai ia 'scissors'
8) kaa gai 'word'
9) kao ba bai 'almost fell'
10) bii gao baa 'commonly called'