As a heads up, this sort of question is great for the Short Answers to Simple Questions thread.

"Weighing of the heart" is a modern term for the practice depicted in Egyptian funerary papyri. The Egyptians preferred to reference the scale itself rather than the process of weighing. For example, spell 30B of the Book of the Dead instructs the heart not to testify against its owner in the presence of the keeper of the balance (Egyptian iry-mḫAt), i.e. Anubis.

O my heart of my mother! O my heart of my mother! O my heart of my different forms! Do not stand up as a witness against me, do not be opposed to me in the tribunal, and do not be hostile to me in the presence of the Keeper of the Balance, for you are my ka which was in my body, the protector who made my members healthy. Go forth to the happy place to which we speed, and do not make my name stink to the Entourage who make men. Do not tell lies about me in the present of the god. It is indeed well that you should hear!

Setne II, which dates to the Greco-Roman period, references the weighing of good and bad deeds, not quite the same as the weighing of the heart.

They entered the seventh hall, and Setne saw the mysterious form of Osiris, the great god, seated on his throne of fine gold, crowned with the atef-crown. Anubis, the great god, was on his left, the great god Thoth was on his right, and the gods of the tribunal of the inhabitants of the netherworld stood on his left and right. The balance stood in the center before them, and they weighed the good deeds against the misdeeds, Thoth, the great god, writing, while Anubis gave the information to his colleague.

He who would be found to have more misdeeds than good deeds [is handed over] to the Devourer, who belongs to the lord of the netherworld. His ba is destroyed together with his body, and he is not allowed to breathe ever again.

He who would be found to have more good deeds than misdeeds is taken in among the gods of the tribunal of the lord of the netherworld, while his ba goes to the sky together with the august spirits.

He who would be found to have good deeds equal to his misdeeds is taken in among the excellent spirits who serve Sokar-Osiris.

The Egyptian word for heart is ib, and the typical verb for "to weigh" is fAi, which also has related meanings such as "to carry/lift." One could therefore translate "weighing of the heart" into Egyptian as fAt ib, -t being the infinitival ending for third weak verbs.

The standard dictionary for those first learning Egyptian is Faulkner's A Concise Dictionary of Middle Egyptian.

The Egyptian language is split into 5 general phases; Old, Middle, Late, Demotix and Coptic. If you're looking for a simple way to roughly look up English to Egyptian phrases then Shenum's "English-Egyptian Index of Faulkner's Concise Dictionary of Middle Egyptian" is the place for you. The best general Ancient Egypian dictionary is "Die Wörterbuch der Ägyptischen Sprache" an Egyptian to German dictionary with lots of useful bibliographic information. The best Old Egyptian dictionary is Rainer Hannig's "Ägyptsches Wörterbuch I." The best Middle Egyptian to English dictionary is William Faulkner's "Concise Dictionary of Middle Egyptian". The best Late Egyptian to English dictionary is Leonard Lesco's "A Dictionary of Late Egyptian." The best Demotic Egyptian dictionary is Janet Johnson's "The Demotic Dictionary of the Oriental Institute of the University of Chicago." The best Coptic dictionary is W. E. Crum's "A Coptic Dictionary."

As for a translation of "the weighing of the heart" that's more difficult to provide. Something like fA.t ib or wdn Hr ib might equate to "weighing of the heart" but the phrase itself is never used (as far as I have seen in my readings of "the Chapters of Coming Forth by Day", the text which the "Weighing of the Heart" is detailed in). Instead, the vignet is called by the Egyptians "The Chapter of not allowing to be repulsed from (owner's name) his heart in the netherworld."

Edit: just noticed the previous answer which did not display initially when I looked at this post, but I hope this expansion of the subject helps.