If I am analyzing a poem and I realize that it has rising meter, what does that say about the poem. Like do happy tone poems have rising meters whereas sad poems have falling meter?
I don't believe there is much you can conclude about a poem from whether the meter is rising and falling. There are happy poems and sad poems in iambic meters, and there are happy poems and sad poems in trochaic meters. It's not like minor and major keys in music.
For example, several of A.E Housman's poems are in trochaic tetrameter, and there doesn't seem to be any consistency in themes.
To illustrate this point, the following two Housman poems have exactly the same meter.
On the idle hill of summer is a depressing anti-war poem. An excerpt:
Far and near and low and louder
On the roads of earth go by,
Dear to friends and food for powder,
Soldiers marching, all to die.
And Reveille is a fairly cheerful seize-the-day poem. An excerpt:
Up, lad, up, 'tis late for lying:
Hear the drums of morning play;
Hark, the empty highways crying
"Who'll beyond the hills away?"