A difficult burden, task, or responsibility. In law, the word onus refers to the burden of proof, as in The onus is on the plaintiff to prove the theory of the case.
He proposed to call witnesses to show how the prisoner, a profligate and spendthrift, had been at the end of his financial tether, and had also been carrying on an intrigue with a certain Mrs. Raikes, a neighbouring farmer's wife. This having come to his stepmother's ears, she taxed him with it on the afternoon before her death, and a quarrel ensued, part of which was overheard. On the previous day, the prisoner had purchased strychnine at the village chemist's shop, wearing a disguise by means of which he hoped to throw the onus of the crime upon another man—to wit, Mrs. Inglethorp's husband, of whom he had been bitterly jealous. Luckily for Mr. Inglethorp, he had been able to produce an unimpeachable alibi.
—Agatha Christie The Mysterious Affair at Styles (1924)