Physical object, carried by a person, that represents an encumbrance
The term millstone is often used to reflect such a burden
A heavy and inescapable responsibility: she threatened to become a millstone around his neck
Oxford Dictionary Online
There is the term dead weight
Defined by The Free Dictionary as:
- an oppressive burden; encumbrance
It can be used to refer to extra weight with no benefit. For example you might ask someone,
"Why are you carrying around all that dead weight?"