lug
To carry or drag something heavy with difficulty.
To lug means to carry or drag something heavy with difficulty and effort. When you lug your overstuffed backpack up three flights of stairs, you can feel the weight pulling on your shoulders with each step. When your family lugs suitcases through the airport, you're hauling them along even though they're awkward and tiring to move.
The word captures both the heaviness of what you're carrying and the struggle involved. You wouldn't say you're lugging a pencil, but you might lug a bag of sports equipment, lug a cooler full of drinks to a picnic, or lug boxes of books to your new bedroom. There's always strain in lugging: your muscles work hard, you might need to stop and rest, and you're relieved when you finally set the load down.
Sometimes people use lug to describe bringing something along unnecessarily, like lugging a heavy winter coat on a warm day. The word emphasizes that whatever you're moving feels like a burden, whether because of its actual weight or because it's inconvenient to transport.