Most tonneau covers weigh around 100lbs, although this will depend on the material as soft materials will weigh less. Plastic covers generally weigh 25lbs, and this answer will always vary based on the thickness, durability and type of material used.
Tonneau covers and most bed rails use the same connection points, so the two will not work together. Some trucks, however, do provide additional connection points, so you need to take a good look at your vehicle to determine compatibility. It's also important to consider this idea from a design perspective as you may not like the way it looks, so you have to put some thought into this before you buy bed rails.
Some tonneau covers are waterproof, although the chemicals used in some car washes are problematic as they will not mix well with the surface material of your cover. In most cases, it is recommended that you remove your tonneau cover before going through a car wash. If you find that this process is a hassle, look at your owner's manual for a detailed explanation regarding this matter.
Tonneau covers reduce the amount of aerodynamic drag because the truck bed contains a bowl that can catch a great deal of wind. This will increase the amount of drag, so it's a great reason to buy a softcover as it will pay for itself very fast, although this is not true for hardcovers, so keep that in mind. If you decide to use a softcover variant, make sure it is extra secure; otherwise, it can fly off into the wind.
If you are using a soft tonneau cover, there should not be any sagging on either side of your truck bed, and you have to adjust the tension adjusters to ensure they are firm. Failure to take these steps will result in you redoing all of your work.
You should give the bars back for a replacement if they are still under warranty when this happens. If you continue to experience this problem even after a replacement, it can be the result of a design flaw. You should think about asking for another type of cover or even asking for your money back, as your tonneau cover should not keep popping open. If your warranty no longer applies, check the tensioning and try repositioning your cover.