This probably doesn't answer your question. Some possible alternatives...
Have you considered CSS instead:
background: linear-gradient(45deg, #3d667c, #1d283e);
Or perhaps you could use the SVG base64 technique (generator tool here):
<svg xmlns="http://www.w3.org/2000/svg" width="100%" height="100%" viewBox="0 0 1 1" preserveAspectRatio="none"><linearGradient id="g932" gradientUnits="userSpaceOnUse" x1="0%" y1="0%" x2="100%" y2="100%"><stop stop-color="#3D667C" offset="0"/><stop stop-color="#1D283E" offset="1"/></linearGradient><rect x="0" y="0" width="1" height="1" fill="url(#g932)" /></svg>
background-image:url(data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIHZpZXdCb3g9IjAgMCAxIDEiIHByZXNlcnZlQXNwZWN0UmF0aW89Im5vbmUiPgo8bGluZWFyR3JhZGllbnQgaWQ9Imc5MzIiIGdyYWRpZW50VW5pdHM9InVzZXJTcGFjZU9uVXNlIiB4MT0iMCUiIHkxPSIwJSIgeDI9IjEwMCUiIHkyPSIxMDAlIj4KPHN0b3Agc3RvcC1jb2xvcj0iIzNENjY3QyIgb2Zmc2V0PSIwIi8+PHN0b3Agc3RvcC1jb2xvcj0iIzFEMjgzRSIgb2Zmc2V0PSIxIi8+CjwvbGluZWFyR3JhZGllbnQ+CjxyZWN0IHg9IjAiIHk9IjAiIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIGZpbGw9InVybCgjZzkzMikiIC8+Cjwvc3ZnPg==);
Have you tried using an even smaller PNG and allowing the browser's native up-scaling algorithm to enlarge it? This might get the file size down as well as eliminate JPG artifacts.
.SVG
? as they're tiny