Giving a pet a weapon doesn't subtract the weight from inventory.

[McPuffin]

Giving a weapon to a pet doesn't remove the weight from your inventory.

[McPuffin]

Does your pet have arms?

Its a skeleton, so I guess it does... i mean it has arm bones at least.

[fash]

If you pick and drop some other item, does it self-correct?

[McPuffin]

Does the skeleton have connective tissue?

*squints closely* Only faint remenants. Is this going to be an issue? Can I still get a refund sir?

[McPuffin]

If you pick and drop some other item, does it self-correct?

Just tested this, and yes it fixes the issue.