Explanation:

- We know the average weight of the first thirteen people is 78 kg. So their total weight is 13 x 78 kg = 1014 kg.

- Let’s denote the average weight of all fourteen people as \( x \).

- We need to use the information that the 14th person's weight is 39 kg more than this overall average weight, so the 14th person's weight is \( x + 39 \) kg.

- The total weight of all fourteen people can be expressed as \( 1014 + (x + 39) = 14x \).

- Solving for \( x \): \( 1014 + x + 39 = 14x \), thus \( 1053 = 13x \), hence \( x = 81 \) kg.

- The weight of the 14th person is \( x + 39 = 81 + 39 = 120 \) kg.

- Thus, the weight of the 14th person is 120 kg.

Option 4: 120 kg