According to the tooltips, weight does impact sneaking. I haven't noticed anything, but I haven't really looked into it. I believe there are probably penalties based on certain thresholds, but I doubt that the ultralight function has as much impact on sneaking as it does on your ability to carry more weight and add action points.
In all likelihood, Muffled is the superiour choice for sneaking, but that is a guess.
If you have invested perks in sneak, you probably don't need muffle (and may not even notice its benefit, if your sneak rank is high enough.) Most likely, muffle is primarily useful for character with minimal investment in sneak, as a way of making it easier for them to get around.
Would be curious if anyone who has experimented can offer any insight.
Muffled, and shadowed.
Ultra-lightweight is focused for VATS use, rather than sneaking. Weight reduction is pointless if you load up with gear and junk, which is inevitable.
Ultra lightweight reduces sound (weight=sound) from the piece you are modding, muffled provides an overall bonus.
On an outfit with only legs, such as Atom Cats, Ultra light is superior on the heavier armors, sturdy synth, heavy combat, ect.
On a full armor set, and lighter armor combos the muffled legs provide a superior bonus.
In my experience, Muffled is the superior mod for sneaking. I've always taken the ultra-light mod to have more to do with carry capacity. The bonus from the muffled mods is canceled out regardless as far as I can tell once you level up your sneak though.
I'm not sure if it really makes that much difference. My current build has high agility but only goes for Ultra-light armor mods and has no problem with sneaking. I noticed how fast I move while sneaking is what counts.
Leather armors, shadowed mod, Sneak perk #4 (nullifies sound from running while sneaking, pretty much making the muffled mod unnecessary), Sneak bobblehead, ten copies of the US Army Special Ops journal (pretty easy to get, mostly just from going to regular quest sites), and you're set. Frankly, once you get that stuff all in order, you'll barely notice a difference if you move up to shadowed combat armor, instead of leathers. Other great armor mods to tack on- Dense (greatly reduces explosion damage), Sleek (increases sneak speed- nice for moving in and killing faster while sneaking), Lead Lined (reduces a lot of radiation damage), Cushioned (reduces falling damage so you can drop off higher roofs without hurting yourself as much, if at all), and Stabilized (if you are into sniping, helps get rid of scope movement).
Oh, almost forgot maxing out Agility. Or at least get it up to 7+, for better results.
You always have to be careful in broad daylight and out in the open, but in optimal sneaking conditions, these things will make you The Silent Death.