I have some swamp milkweed here, and I'm coming across a problem that I had last year as well. These are two year old seedlings I've grown from seed, and last year later in the year the green leaves of my plants started to get lots of small yellow spots starting from the leaf base and spreading out. The leaves would brown in the meantime as the leaves seem to dry and curl upwards; this is where I noticed webbing like cobwebs on the plant from the curling leaves up to the stalk.
I've been having problems with yellow aphids on these plants, and I've used pesticide. I've used two kinds because at first I thought that might've been the problem. One was organic and the other was an ortho flower and rose care spray.
This year, this problem is showing up again, but instead of later on in the year it's happening now. I've been clipping the stalk off at the bottom when this happens; I did this last year, and the plants started to grow back out this spring. I used the pesticide for aphids because they showed up (the flower and rose kind) about two weeks ago, so this time it's not an immediate occurrence.
Is this a disease? Or perhaps a soil issue? I just repotted these plants this spring when they were starting to grow out (4 plants per 10 inch pot), and they have filled up the pots with their roots. So they have seemed healthy till now except for the aphid problem.
The webbing is often associated with tiny critters called spider mites. These are not true insects since they have 8 legs. They are tiny- like a pin point. They produce the webbing along the leaf stems (in the crotch of the leaf). Enough of them can literally burn up the leaves. They are common in hot/dry weather. An easy check for spider mites-- tap or shake a few affected leaves over a piece of white paper- like an index card. Do this a few times and look for the tiny orangeish/yellow crawling on the white paper. They show up pretty good with white in the background.
You may consider using an insecticidal soap for spider mites and aphids. Check for this product at your garden center. Some people use a strong stream of water to literally wash these critters off the plant..
From your description, it doesn't sound like a disease, but aphids and spider mites. You can also collect a few affected leaves and carry them to your local garden center (not the big box stores)and let them look at the leaves for these aphids and spider mites.