Generally speaking, attach too much significance to [something] can be replaced overvalue, but that doesn't sit well with me in certain contexts.
For example, suppose I reached some conclusion after considering various factors, but it turns out later that I accorded too much weight to "Factor X" (causing me to reach the wrong conclusion).
"I attached/ascribed/assigned/etc. too much significance to X" conveys exactly what I want to say. I can't explain why "I overvalued X" doesn't cut it for me - that's just the way it is.
Words such as overstate, overplay, overemphasise all seem to imply I focused too much on X in a debate attempting to defend my (erroneous) conclusion. And overestimate implies mistakenly thinking X was bigger than it really was (rather than just "more important than it should be").
Ideally, I'm looking for "I xxxx'ed X", but even "I xxxx'ed the importance of X" would do.