We are given that:

• Weight of 6 boys = Weight of 7 girls = Weight of 3 men = Weight of 4 women.
• The average weight of women is $63$ kg.

First, calculate the total weight of the 4 women: Total weight of women = $4 \times 63 = 252$ kg.

Now, the weight of 6 boys equals the weight of 4 women, which is $252$ kg.

Thus, the total weight of 6 boys is $252$ kg, and the average weight of the boys is: Average weight of boys = $252 \div 6 = 42$ kg.

Answer: B. $42$ kg