TWar weight vs home v

This question is not very clear, but will attempt to answer to the best of my ability.

does home village weight equal war base weight if changes are only made on the home village?

I'm not sure what changes are being referred to, but any upgrades applied to Home Village are mirrored in War. The only difference is the layout of buildings, which has no affect on weight.

Does the added weight on your home village just add to your war base irrespective of changes you've made?

Again, not sure about what "changes" but any upgrades on Home Village apply to War Village.

or does the war weight only adjust once your war base is updated?

The war base updates instantaneously.