Chords can have different inversions which alter the "feel" of the chord. For example chords can have different notes in their bass. Here is 3 different inversions of C Major.
"C Major, with a C in the Bass"- This is a strong solid chord. "C Major, with a E in the Bass"- This is more of a passing chord and would not be used in a cadence. "C Major, with a G in the Bass"- As above
When these "weaked" inversions are used, they can imply different things. In most music, they are just used as part of a harmonic progression. In other pieces, such as choral pieces, an inversion can be placed under certain words to reiterate the meaning of the text. For example if the libretto is unsure and ambiguous the composer could use weaker inversions to emphasize this.