I've had problems with insomnia too but wasn't sure if it was switching to the e-cig or the fact that I have an autoimmune disease that effects my thyroid. I have cycled between sleeping a lot and insomnia for most of my life. Mine is starting to go away, but I couldn't tell you if this is because I've slowed down my vaping, or because my doc is currently messing with my medication since my numbers were off the last time I went in.
If you think about it, our bodies are going to react differently to e-cigs because we are now getting our nicotine without smothering ourselves with carbon monoxide and other nasty chemicals. It would make sense that with tobacco cigarettes there is sort of a balancing effect. Although the nicotine is stimulating your system, carbon monoxide causes sleepiness, so you might not notice the stimulant effect quite as much.
People have also mentioned sleep disturbances with the patches. Not only can insomnia be a problem, but also vivid dreams and frequent episodes of waking during the night.
As to weight loss, studies have shown that nicotine combines with several neurotransmitters that control appetite, so you don't feel as hungry using it. Even mice who were taken off IV nicotine showed similar weight gain to humans who had quit smoking. In fact, I've seen it stated a number of times that hunger and nicotine withdrawal can be easily confused. I also wonder if there isn't something to the hand to mouth thing though. It's just so much easier to vape an e-cig or light a cigarette than go to the kitchen and rummage around for something to eat.
Anyway, the point of all my rambling is that I think the others are giving good advice in that either dropping your nic levels or slowing down how much you vape at night would help the insomnia. As to the weight loss issues, a permanent drop in nic levels might help. You might also try to eat a small amount of something rather than picking up your e-cig when you start feeling the urge to vape, to see if you might actually be hungry instead of nicotine deprived. Or, you could try to keep your vaping closer to a smoking schedule. I know personally I had to stop myself from getting into the habit of having my e-cig with me wherever I was at the moment because I tend to pick it up and vape without realizing I'm doing it. Of course I did the same thing with cigarettes which is why I instituted my own "smoking area".

