Does a grandfather's will to cover the costs of his grandson's marriage, without it being written down and with his subsequent death, obligate his heirs to pay these costs, knowing that there were witnesses who heard his will?

A bequest is established by a form of words indicating ownership after death. The form of words mentioned here could be a bequest or a promise of a gift during life. What matters is what the witnesses understood. The testimony of ascendants and descendants for one another is not accepted, except for an uncle. However, his testimony alone is not sufficient to prove the bequest; it is sufficient with the claimant's oath. If you are certain of your grandfather's intention to make a bequest, and your uncle testifies that he understood this, then the bequest is yours based on your oath and your uncle's testimony. If some of the heirs acknowledge it but not others, it is enforced against the acknowledging heir in proportion to his share. In case of dispute, the matter is referred to the Sharia court.