I don't mean to be rude, but you're not really thinking this through. What would happen to a golfer's swing if you attached two kilograms to his club? Or a tennis player's racket? It would throw off the instrument's center of gravity and completely change its balance, right? Making it about as agile as, well, a five pound weight? And the user's arm would tire much quicker than without the added weight. The same is true for bows, only more so, because such a device would probably interfere with the pull. Even if you could accommodate that, the weight is going to kill the archer's efficiency. When shooting a bow, you grasp the stave with one hand while the other manipulates the arrows and the bowstring. Try holding two or three kilograms in your outstretched hand. See how long you can hold it there before your arm starts to tremble. And these were already very, very stout bows which required a great deal of strength and endurance to shoot rapidly. The protection of a relatively small shield (what happens if the arrow arcs down on you? what if it strikes your leg?) would be outweighed by the gross inconvenience to the user.

This is not to say that archers never used shields. They certainly did. Longbowmen very frequently carried small bucklers for close-in fighting. French crossbowmen typically brought shield bearers along who held large shields called pavises for the crossbowmen to shelter behind.