Yes, I would say it generally costs more. But it doesn't have to.
For example, ultralight tents are expensive, so I embraced tarp life. My tarp and bivy are lighter than most UL tents and cost hundreds of dollars less.
My individual pieces of clothing cost more, but adopting an ultralight approach means I don't carry needless extras, so I don't buy as many clothes in the first place.
UL stoves can cost a lot, but the BRS stove or an alcohol stove are cheap and weigh less. Eating cold food is even lighter.
You get the idea. It costs exactly what you spend on it. It can be done affordabley if you are strict about what you are carrying and strategic with purchases. Leaving unneeded items at home will have a bigger impact on your base weight than any $700 tent.
I did at one point. Let me see if I can track it down. Fair warning, part of my UL motivation is saving weight for luxuries like a kindle and deodorant.
We had a baby in March so I haven't been on a trip since last fall. Hoping to do a few more sections of the MST this September.
Edit: I found my old lighterpack account, but the most recent packing list is from a few years ago. I should probably be responsible and make one for current trips. I'll send you another reply in a day or two with an update.
In the meantime here's my lighter pack from a lightweight hammock trip.. I've since decided I prefer the ground and switched to a quilt, pad, tarp, and bivy. I traded the pocket rocket for an alcohol stove (safe over here in the super damp southern US). I also cut some unnecessary weight from the FAC, cooking tools, ditty bag, etc.