Usually it's to do with the lens, and the width is determined by the focal length, which is the number with mm after it printed on the lens. So an 18-55mm lens will go from 18mm (the most zoomed out) to 55mm (the most zoomed in). Or a 50mm lens is fixed at 50mm (that type of lens is usually touted as the best one for portraits).
As you get lower, you get more distortion (fisheye effect) so using the highest focal length you can is usually recommended.
In my experience the camera body isn't the heavy part, although I use the Canon Eos range which is fairly lightweight (coincidentally, it's what we have at work as well as what I have at home). The lenses tend to be the heaviest part of the setup IME, especially if you're carrying around more than one.
If you don't want to carry lenses around, you can do wide-angle shots with a normal lens. For very wide angles without needing a wide angle lens, one common technique is to set up your tripod, and take multiple pictures at a higher focal length so you get all the detail with less distortion.
Then you can "knit" these pictures together in Photoshop (just last week I did a 16-photo panorama shot this way which produced a great quality image). You can do it with anything from 2 upwards with a half decent computer processor these days which saves on the weight of lugging a lens around.
But if you do want a wide angle lens, I recommend getting one that starts around 12mm for minimum distortion but the ability to fit a really decent amount into the shot.
If you're not looking to do "professional" photography, though, have you considered a bridge camera as a more lightweight alternative? They can produce very nice photos without needing all the kit for a heavier DSLR (or mirrorless) camera.