Compression tights and shorts
I'm definitely no expert on clothing (of any type) but my sense is that manufacturers of compression tights and shorts have "base layer" as intent. Nonetheless, one can use them for other things like weightlifting.
I wear compression shorts and tights while training. I buy the cheapest I can find, which I assume are among the thinnest you can find. They all work fine for me. Heavier material might last longer, but my habit is to buy training clothes each year. I have yet to throw out any in the two years I have been using them
I train in my garage. In the winter it gets down to freezing in my gym. Occasionally I have to wear gloves, but the rest of me is fine.
Compression briefs under compression tights? Makes no sense to me.