I realised recently that during weight training there is much benefit to be gained from have a strong 'core'.

Previously, I would perform squats or other exercises without thoughtful emphasis on keeping the core tight. More recently, I have attempted to resolve this during exercise movements.

I believe so far that it has been beneficial in allowing me to incorporate heavy exercises back into my program (back injury recently).

I definitely feel that the evidence around this topic is lacking, but, there is benefit to be gained from strengthening the core.