"...Influence (mainly..).."
.
.
Hard evidence for this?

Take your time.

As for permanent membership expansion, once it gets beyond say 10, the effectiveness would dissolve.

Canada would be in line though, behind Brazil, India, Japan,Nigeria, Indonesia, Germany, Mexico, Pakistan, Iran, Mexico, South Korea......and many others that have population (all), economy size (nearly all, and or geography (Nigeria, Egypt, South Africa)