To carry something or someone on one's back (e.g., a backpack or a child).
子どもを背負って公園へ行った。
I went to the park carrying my child on my back.
旅行のときは重いリュックを背負うことが多い。
When I travel I often carry a heavy backpack.
荷物を全部自分で背負う必要はないよ。手伝おうか？
You don't have to carry all the luggage yourself. Shall I help?
To take on a burden or responsibility; to assume liability or obligation.
このプロジェクトの責任を彼が背負うことになった。
He ended up taking responsibility for this project.
会社の借金を一人で背負うのは重すぎる。
It's too heavy for one person to shoulder the company's debts alone.
監督はチーム全体の期待を背負って試合に臨んだ。
The coach faced the match carrying the expectations of the whole team.
To have something at one's back or in the background—literally or figuratively (e.g., being backed by something, or a house having a mountain behind it).
あの家は山を背負って建っている。
That house stands with a mountain behind it.
彼は老舗の看板を背負って営業しているので期待が高い。
He runs the business backed by a long-established brand, so expectations are high.
このチームは地域の応援を背負って戦っている。
This team is competing while carrying the support of the local community.
Colloquial: to act conceited or show off—often seen in contracted forms like しょってる.
あいつ、いつも自分の武勇伝をしょってるよね。
That guy is always bragging about his exploits.
ちょっと成果が出ただけでしょってるのは見ていて気持ちいいものじゃない。
It's not pleasant to watch someone act high-and-mighty just because they had a little success.