there are many many different "shipping containers". I think you mean Intermodal containers, which come in different standard sizes.
picking the 40 foot one, that is 40x8x8.5 ft
weight 8,380 lb
volume is 2720 ft³
max gross weight 66,139 lb or 33 tons
weight of that volume of water is 2720 ft³ x 62.1 lb/ft³ = 169000 lb
so the weight of the contents, if it barely floats, is 169000 – 8,380 = 161000 lb, 80 tons
given that the specified max gross weight is 33 tons, they ALL WILL FLOAT... until water seeps in, and then they sink. Unless the contents are something that traps air, such as ping-pong balls. Or something that has low enough density to offset the weight of the container, such as wood. or styrofoam cups.
density of fresh water at 20C = 0.998 g/cm³
= 998 kg/m³ = 8.33 lb/gal = 62.1 lb/ft³