When an object is lightweight, it weighs much less than other similar objects. A person is a lightweight if they can't handle much — if you get full after a small meal, big eaters might refer to you as a lightweight.
Break lightweight apart — light + weight — and you see its definition right there in its root words. Someone who is called a lightweight is either a professional boxer who weighs under 135 pounds or he's someone with little importance or ability. When a company is looking to make layoffs, it's the lightweight employees, or those who just aren't important to the business that often get axed first.