Well:
TONE:
In most languages the major component of stress
is pitch.
A language whose stress system is a tone system and whose tone system is used just for stress is called "a pitch-accent language". Classical Ancient Greek was one of those.
It sounds like you want your language to have "morphological tone"; that is, the tone-pattern with which you pronounce a word can inflect it into different forms of the same word. English does a little of that; the noun "object" and the verb "object" differ in which syllable gets the stress, and if you listen closely you'll see that's mostly a pitch difference. Although actually the stressed syllable is usually longer and louder as well, try to pronounce it only longer and not louder nor higher pitched, then only louder and not longer nor higher pitched, then only higher pitched and not longer nor louder, and see what's easiest to notice. My bet is that pitch is easiest and volume is most difficult, with time in between.
Some languages have "lexical tone", where the tone-pattern can mean a completely different root. In such languages, if there's stress, it probably isn't mostly pitch.
English mostly uses tone over entire clauses, or sometimes multi-word phrases shorter than a whole clause. Questions tend to rise in pitch at the end; commands and declarations tend to fall in pitch at the end. I forgot what that's called, but it's neither lexical nor morphological.
There may be such a thing as phonemic tone too; I can't remember for certain.
More languages use tone for something than don't, though it's awfully close to half-and-half.
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MORAE:
See this link:
STRESSTYP
Languages that have stress -- that is, most of them -- have various means for deciding what syllable of two-or-more-syllable-words to put the primary stress on, and which syllable(s), if any, of three-or-more-syllable words to put secondary stresses on.
If all syllables are treated the same in these two processes, that language's system is not weight-sensitive.
But for some languages there's a definite rank in how likely a syllable is to get stress and in how much influence it has on the placement of stress.
If there are just two levels for such a language, some syllables are "light" and some are "heavy".
A "light" syllable is said to have one mora; a "heavy" syllable is said to have two morae.
If a language has three or more levels, all those heavier than "heavy" are called "superheavy", and are said to have three (or more) morae.
What a mora is depends on the language; every language is free to define it differently from any other.
So to that degree, yes, it's totally arbitrary.
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For languages with weight-sensitive stress and two weights, ordinarily a syllable's onset doesn't affect its weight one way or another; the weight
(in most such languages) depends entirely on the rime (the nucleus and the coda).
Suppose all a language's syllables are open (no codas) and all vowels are monophthongs (no diphthongs), but some are short and some are long (vowels have phonemic length).
Then in that language, syllables with a short vowel are light and those with a long vowel are heavy.
Now suppose again that all a language's syllables are open (no codas), but now suppose all vowels are short, but some are monophthongs and some are diphthongs.
Then in that language, syllables with a monophthong are light and those with a diphthong are heavy.
A third example; suppose all the vowels are short monophthongs and all the codas are single consonants (no coda clusters).
Then in that language, open syllables -- those without a coda -- are light; syllables with a sonorant coda (nasal or liquid or semivowel or glide) are heavy. Whether other closed syllables are light or heavy will depend on the language.
Other things can happen too. Maltese, for example, counts any syllable with a non-cluster coda as light, and any syllable with a coda-cluster as heavy.
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What's heavy and what's light depends on the language.
If your language has long vowels and diphthongs and closed syllables, usually any one of those is enough to make the syllable heavy.
You can be sure that an open syllable with a short monophthong vowel is light.
The difference the coda makes varies from language to language. Ordinarily coda-clusters make the syllable heavy; ordinarily sonorant codas make the syllable heavy. But whether single-consonant non-sonorant codas make the syllable heavy, depends on the language.