Not at all, not even a little bit. I've had my D5200 for over two years now and I love it. I started with just the camera and the 18-55 kit lens, and recently added the Tokina 11-16mm ATX Pro DX II ultrawide. The kit lens allowed me to take much better pictures than I'd ever taken with any cell phone or point and shoot camera, while still offering enough versatility to help me determine what direction I wanted to go.
For me it is a hobby too, I really enjoy it and I love the reaction I get from some people when I show them a great pic. But I go out specifically with the intent of taking pictures, so bringing the camera with me isn't a drag. I have a comfortable sling bag, makes it easy to bring all my stuff whether walking or biking, without any discomfort. I don't really get tired of having it on me at all. It obviously is bigger than a phone or a compact, but it doesn't seem too bulky to me.
If you're looking for something that you can have on you all the time without feeling like you're lugging around a camera, then a DSLR might not be for you. There are some great compacts like the RX100 that might better suit your needs.
Or maybe you just haven't found the bag that makes you forget you're carrying anything. They are not point and shoot cameras though, so you may be better off with one if that is the type of user experience you're looking for.