I carry siege shields sometimes because they're pretty useful and I have 2 slots free anyway. 25 weight makes them really heavy, so even though I have 8 athletics and light gear I'm still slower than most people when carrying one.
If I get into a dangerous situation I just lose the shield so that I can maneuver better or escape. I've even ditched my weapon before. In my mind it's like dropping ballast.
Someone might steal your stuff before you can come back for it, but that's better than dying with a bunch of extra ammo isn't it? Especially since you can also find another weapon or more ammo later if you run out.