This might help ... from the FAQ in the Cheats, Hints, and Spoilers forum:
Q) There seems to be something wrong with my weight/encumberance. What can I do about it?
This appears to be some sort of bug. There has been given an explanation and solution by a certain user whose name is now lost. But here's his post [his Real name appears to be Josh]:
If your weight is too high, the fix is easy. Drop everything out of inventory, pull down the console and type the following commands. I'll assume your weight is 126 heavy for this example:
player->additem "misc_soulgem_common" 1
player->removeitem ""misc_soulgem_common" 127
Now your weight is right Trust me, it works.
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If your weight is LOW, the solution is harder, but will still only take a little time. Again, I'm assuming you are too light by 126 here
First, go in to the editor and create a mod that makes misc_soulgem_common weigh 127. Save this mod as weightfix.
Load up your game using the new mod, drop everything, using the console type
player->additem "misc_soulgem_common" 1
Your weight will now be 1 with a 127 pound soulgem
now save and exit.
Un-select your mod from datafiles, you can delete it now.
Re-load and your weight be 1 with a 1 pound soulgem.
Problem solved. You can do a
player->removeitem ""misc_soulgem_common" 1 to get rid of that soulgem if you want, or you can just drop it