He is under a heavy debt.

他负债累累。

《新英汉大辞典》

His father died, leaving him in heavy debt.

他父亲去世，给他留下大笔债务。

youdao

Heavy debt can also affect a country's competitiveness.

沉重的债务负担还会影响一个国家的竞争力。

youdao

Many banks,he says, are going to need additional capital to deal with bad loans and heavy debt.

VOA: special.2009.05.29

It involves loans, debt guarantees and other support to euro area countries with heavy debts.

VOA: special.2010.05.14

That would be good news for European countries with heavy debt loads.

VOA: special.2010.05.07

He was also in heavy debt to others and feared the bank would reveal them.

BBC: Bedford knifeman Barry Bell guilty of stabbing colleague

Now, it has such heavy debt that the home islands may sink under the weight of it.

FORBES: Dire Consequences As Global Growth Grinds To A Halt

Transocean has been struggling with a heavy debt load that has put pressure on its credit rating.

FORBES: Transocean Forgets Macondo, Focuses On Offshore Market Strength