Step 1: Recall the meaning of average.
The average is the total of all values divided by how many values there are. So if we know the average and the count, we can find the total by multiplying them. \[ \text{Total}=\text{Average}\times\text{Count}. \]
Step 2: Find the total weight of the 24 students.
There are $24$ students with an average weight of $52$ kg. \[ \text{Total weight}=24\times52=1248\text{ kg}. \]
Step 3: Find the new average after the teacher joins.
The average goes up by $1$ kg when the teacher is added. So the new average is \[ 52+1=53\text{ kg}. \]
Step 4: Count the new number of people.
Now there are the $24$ students plus $1$ teacher, which is \[ 24+1=25\text{ people}. \]
Step 5: Find the new total weight.
Multiply the new average by the new count: \[ \text{New total}=25\times53=1325\text{ kg}. \]
Step 6: Find the teacher's weight.
The teacher's weight is the extra weight added, which is the new total minus the old total: \[ 1325-1248=77\text{ kg}. \] \[ \boxed{77\text{ kg}} \]