Here "stand before me" is an idiom that means to continue in Saul's service. Alternate translation: "Let David stay in my service" (See: [[rc://en/ta/man/jit/figs-idiom]])
Here "eyes" are a metonym for sight, and "my sight" represents how Saul judges or evaluates David. Alternate translation: "he has found favor in my judgment" or "I am pleased with him" (See: [[rc://en/ta/man/jit/figs-metonymy]] and [[rc://en/ta/man/jit/figs-metaphor]])