Unfortunately they take up a lot of inventory / chest space, since they are only stackable with the same the weight (I assume that's what the number is) and type. You also have to combine certain types before you can use them.

I haven't yet figured out what happens when you use, say two of the fish types with weight 1 and the third one, is, say weight 5. Do I only get the amount of fish that I would get with 3 weight 1 fish?

It seems like you get a decent amount of fish, so maybe it adds all the numbers together to determine how many you get?