I've stopped kicking the snow/ice packed up behind my wheels, for 2 reasons.
i) It forms semi aerodynamic fairings.
ii) I figure that the ice next to the surfaces can only do so much in the way of corrosion before it's chemically exhausted. What's the point of kicking it off 4 or 5 times a day so you get fresh and more reactive stuff on there, and keep exposing it to air??? Also figure it stays colder at the interface there when you leave it on, which suppresses chemical reaction. If the temperature kicks above zero C for a bit in the middle of the day, it's better that it stays ice coated and sealed in ice than exposed to liquid brine.
I think the weight is insignificant. I'll gouge out some immediately behind the tire though if it looks like rubbing. Only bad thing I can think of really is if it drops off while you're parked and refreezes making ice chocks, but you can usually kick those out, and if you park so you can set off forwards it's no biggie.
Would also rather have briny spray on semi-liquid slushy roads deflecting off those or freezing on them than splashing all up the side of my car.