How much background information should I provide in a paper if it is a follow-up to a previous publication of mine?
I think you need to assume that the reader cannot access your first paper for some reason. If the second contains enough description without it, then that would be acceptable in most fields to refer to the previous work for more details/justification.
However, I would caution against you being the only judge of whether you have enough detail as you are likely too familiar with your own work. If you have a colleague who has not read the first article, that could read a draft for you to give their opinion, I would recommend it.