Adding a weighting factor, or simply weight, to the assessment allows you to take into account the "importance" of the task for which the assessment is made. For example, weight = 1 could be chosen for homework, weight = 3 for a test, and weight = 5 for a final test.
The average grade is calculated as the sum of all grades divided by the number of grades, the weighted average grade, or simply the weighted grade is calculated as the sum of the products of the grades by their weights, divided by the sum of the weights.
Here is an example: 5 for homework (which is assigned a weight of 1) and 3 for a test (which is assigned a weight of 3). Then the average grade = (5 + 3)/2 = 4 points, and the weighted average grade = (5×1 + 3×3)/(1 + 3) = 14/4 = 3.5, which reflects the fact that the test scores is more important than homework grades. The weight can be thought of as the number of corresponding grades - the weighted average grade for a 5 with a weight of 1 and a 3 with a weight of 3 is exactly the same as the average grade for one five and three threes.
The weighted average grade thus demonstrates a more valuable indicator of academic performance.