Such a burden of proof can be impossibly heavy.

Gleaming densely in the moonlight, it appeared impossibly heavy.

The drive was impossibly heavy, much heavier than its size suggested.

Her arms seemed impossibly heavy as she wound them round his neck.

The burden his master had laid upon him seemed impossibly heavy.

The empty white space yawned before her, and the child in her arms seemed impossibly heavy.

Rockets for lifting spaceships were impossibly heavy, for practical use.

His body felt impossibly heavy, and even in the heat he was cold.

The half-melted shield now felt impossibly heavy, weighing his left arm down.

This makes the burden seem impossibly heavy and the conflicts irresolvable.