Usage patterns
〈物〉を持つto carry (one's) luggage
I climbed the stairs carrying my heavy luggage.
〈物〉を預けるto check in / leave one's luggage (with someone)
I checked in my suitcase at the airport.
〈物〉を送るto send a package/parcel
I sent a package to my parents' house.
〈物〉を運ぶto transport/carry luggage or cargo
We transported the luggage by truck.
〈人〉の荷物になるto become a burden to someone
As I get older, I don't want to become a burden to my family.