First, we will need a picture of the weigela. Second, what kind of weed prevention paper did you put down? Many, if not most, kinds of mulch underlayments will do more harm than good to the plants. Third, bindweed is a real pain in the patootie, but I don't believe that it can kill a shrub, so leave that out of your concerns. Unfortunately, getting rid of bindweed is a real undertaking and weed killer is not much good in the effort - you've got to dig up and get rid of the thick white root that all the little vines are coming off of, and you will still get a random one here and there. There is a lot of information on the 'net on getting rid of it, so google it and see what works best for you.

Thank you for your response! I will be sure to take and post a pic of my weigelas once I get home from work. But, here's the weed prevention fabric I bought: http://www.homedepot.com/p/Vigoro-3-ft-x-50-ft-Polyethylene-Weed-Barrier-Landscape-Fabric-1142RV/206684876 

The hot exposure is probably too much for the purple weigela. Also if the bed was liberally amended and the shrub was planted with an intact potting soil root-ball there could be problems with drying out of the roots, despite watering. Poke around in the soil on the plant and near it to see what the soil moisture situation at this time actually is.

If the bindweed is something like Calystegia silvatica it needs to be constantly snapped off and thrown in a yard waste tote or burned - as soon as the shoots appear above the ground, every time. Otherwise it can be killed by repeated spraying with glyphosate but to make use of this method the tops must be left to reach flowering stage before they are big enough that enough chemical will be absorbed to start killing the entire plant.

LOL, Ken I wish we had our own place - I'd tear everything up in a heartbeat and go from there! Clean slate and all. I am in CO, and the soil was very clay-like. I removed a bunch of the existing soil and added in a bunch of well-draining soil at least 6 inches worth and mixed all that goodness up. That may have not been the best way to do things, but like I said everything else is looking good. Soil is draining pretty well. I visit with my babies every day before and after work. Spring in CO? That's a hilarious visual....I've only been in the house almost a month now, but since "Spring," it has snowed and then lead on to pretty dry weather. It hasn't rained much here at all, and my lawn is suffering from drought stress despite my own heavy watering. Rained last night and supposed to rain off and on (hopefully) throughout the weekend.

Yes: you should have kept the replacement soil separate from the existing soil. If you can show pictures of the bindweed - preferably in flower - it can become possible for us here to tell which specific plant you are having to deal with.

Hey, so I am back and have some pics of my situation. The first pic is of what I suspect is the bindweed.

Sorry for the slightly fuzzy pic. The flowers are white with a pinkish center.

Here are the pics of my weigela shrubs (2 different ones). As you can see, the leaves on the bottom portion of the pics (closer to the shrub's stalk....is that the right term?) are dried, brown, brittle. Not sure if this is normal or not. I appreciate the advice.

Probably it's Convolvulus arvensis but another may be possible. Colorado Cooperative Extension may have control recommendations. The weigela I still expect to be sun burned. I wouldn't put a purple form in a hot location anyway because strong sun exposure fades their foliage color.

I agree it looks like Convolvulus arvensis. It's slightly lucky you haven't got one of the climbing ones which are much more egregious. Although annoying it isn't going to harm healthy shrubs. There is something else going on. It does look like some sort of burn damage. What is that curious mulch material?

Pull the bindweed. Just dedicate an hour or two a week toward pulling it, and do so when relaxed and 'zen' enough to take the time to get the roots. Keeping it from flowering is key- you've gotta stay with it.

It's a pain to hand weed but for many situations it is the answer and a couple of days work can clear up a problem you'd otherwise be fighting for years. Just do it, lol.

The mulch looks like rubber mulch and is most likely part of the problem. Wood mulch helps cool the soil and over time breaks down to enrich it. Rubber mulch heats up and any breaking down it does releases chemicals. Not a good choice IMO, especially along with the "weed barrier."