Bottom 大 was added later as a phonetic-and-balance element; it gives the indexing radical (大) and a vague sound hint. The whole-char etymology stays rooted in the upper notched-tally + knife scene; 大 is structural rather than meaning-bearing here.
Upper-left depicts the notched tally stick - three horizontal scratches showing the count carved into a wooden contract piece. Before paper, agreements were recorded by cutting matching notches into a split stick; each party kept half.
Upper-right shows the knife doing the carving. 丰 + 刀 together write the act of notching a contract - the original concrete meaning of 契 before it generalised to any agreement, deed, or rapport.
