Place two weights on each side of the scale, and measure three times, with each time measuring a different pair on each side. For example, measure weights $AB$ vs $CD$, $AC$ vs $BD$, then $AD$ vs $BC$. Two of these measurements will result in one side weighing more, while one will result in both sides being equal. WLOG, let $AB < CD$, $AC < BD$, and $AD = BC$. From this, we know $A$ must equal $1001g$ and $D$ must equal $1005g$. Then compare weights $B$ and $C$ to determine which is heavier. Therefore, you can determine the weight of each with only $4$ measurements.