A large container ship enjoys economies of scale over smaller container ships because the cost of shipping a TEU (twenty-foot equivalent unit) for a day declines as the ship gets larger. This is because the costs of the fuel that the ship consumes each day can be divided up between more TEUs.
The main cost of operating a container ship is the fuel that it uses. Of course, the amount of fuel used is somewhat affected by the weight that the ship carries. However, the effect of the added weight is not large enough to offset the gain in fuel efficiency that comes when more containers are loaded on the ship. This means that costs will decrease as ship size increases, which is the definition of an economy of scale. As we can see in Figure 7 of the paper in this link, a 4000 TEU ship can be more that 20% cheaper to operate (in costs per TEU per day) than a ship that holds 2000 TEU.
Economies of scale in large container ships, then, come from the fact that they use less fuel per TEU per day than smaller ships do.