First, I think theives tools weigh a bit much. 1 unit per? Though I guess there could be strategy involved not carrying 100 of the things around. But I digress. My rogue was heavily burdened so I decided to pass off some of these tools to another character. When I split the stack and gave half of the tools away, my weight didn't change. I had to take the rest of my split stack, give it to another character too, to lose the weight of the pre-split stack. Then finally I had to take the half I wanted back. I tried it with other items too and noticed the same thing

That's because all item have a weight. Game just rounding it down. In case of item with weight less than 1 - it round down it to 0. Of course they still have appropriate weight.
And no, no item should be weightless.
For easitehr weight management there surely will be Bags of Holding in game. Lvl-4 is too soon to give one.

Just checking, but were you moving them from a backpack? I noticed yesterday that when moving items from backpacks, the weight wouldn't update on the UI immediately. When saving and then reloading, it updated.

Nope, my theives tools were siting in my genral inventory. I was 70/60 weight, I split 30 tools into 2 stacks of 15 which should have taken me down to 55/60 when I passed off a stack to another character...except it didn't. I had to pass off both half-stacks take make the entire 30 points disappear, and then I had to take back one of the half-stacks to get the results I wanted.

Odd huh?

For packs and splits I think you need to then drag the item into another persons inventory and then back into yours to update. Its janky.

It seems to be a UI issue moreso. It is actively reducing your weight, as encumbrance is removed, but the UI doesn't update the change unless you remove something from your inventory, or move the item to another players inventory and force it to recalculate everything in your inventory and reflect the new total.

That sounds more likely!