Grease comes to English via Norman grece, from the Old French graisse, from the latin crassus, meaning thick or fat.
Crassus is itself descended from the proto-indo-european *kwert- meaning to weave or twist together. This is similar to the latin cratis meaning wickerwork, or the Sanskrit कृत्, kṛt meaning to spin. Note that in Sanskrit ṛ is a vowel, pronounced like ri in Northern India, and ru in Southern India. An example of this usage, the god Krishna should be written as Kṛṣṇa. Cratis in Latin also provides us with the English word ‘grate’ as well.
Another word descended from crassus in English is crass, meaning rude or dense, into English via French crasse.