Jon caught four fish that weighed a total of 252 pounds. the kingfish weighed twice as much as the amberjack and the white marlin weighed twice as much as the kingfish. the weight of the tarpon was 5 times the weight of the amberjack. how much did each fish weigh?

1 Amberjack 
Kingfish equals 2 Amberjacks
Marlin equals 2 Kingfish or 4 Amberjacks
Tarpon equals 5 AmberJacks

So:
1A plus 2A plus 4A plus 5A equals the 252.
(where A is weight of the AmberJack).

Therefore:
12A equals 252, and A is 21. (252/12 = 21)

Then:
The Amberjack is 21Ibs.
The Kingfish (twice as much as A) is 42Ibs.
The Marlin (four times A) is 84Ibs.
And the Tarpon (five times A) is 105Ibs. 

To Check:
21 + 42 + 84 + 105 = 252