Пример на Github

Рабочий пример @ManyToMany c дополнительной колонкой можно найти тут

На данный момент есть проблема с удалением объекта, в который вложен один или несколько объектов.

Update 1

Проблема с удалением нескольких объектов почти решена. Осталось добавить каскадное удаление объектов.

Основные требования:

1. Не использовать @Data Lombok'a. Проблема связана с @EqualsAndHashCode. Ссылки на источники о данной вещи найдете в этом вопросе
2. equals, addTag/Post, removeTag/Post должны быть записаны так же как и в примере ниже. Без них невозможно соединение двух сущностей.

Правильная запись кода

Dish.java

@Entity
@Getter
@Setter
@Table
public class Dish{

    @Id
    @GeneratedValue(strategy = GenerationType.SEQUENCE, generator = "dish_generator")
    @SequenceGenerator(name="dish_generator", sequenceName = "seq_dish", allocationSize = 1)
    private Long id;

    @Column
    private String name;

    @OneToMany(
            mappedBy = "dish",
            cascade = CascadeType.ALL,
            orphanRemoval = true
    )
    List<DishSize> dishSizes = new ArrayList<>();

    public void addProduct(Product product, Integer size) {
        DishSize dishSize = new DishSize(product,this,size);
        dishSizes.add(dishSize);
        product.getDishSizes().add(dishSize);
    }

    public void removeProduct(Product product) {
        for (Iterator<DishSize> iterator = dishSizes.iterator(); iterator.hasNext(); ) {
            DishSize dishSize = iterator.next();

            if (dishSize.getDish().equals(this) &&
                    dishSize.getProduct().equals(product)) {
                iterator.remove();
                dishSize.getProduct().getDishSizes().remove(dishSize);
                dishSize.setProduct(null);
                dishSize.setDish(null);
            }
        }
    }

    @Override
    public boolean equals(Object obj) {
        if (this == obj) return true;
        if (obj == null || getClass() != obj.getClass()) return false;

        Dish other = (Dish) obj;
        return id != null && id.equals(other.getId());
    }

    @Override
    public int hashCode() {
        return Objects.hash(name);
    }
}

DishSize.java

@Entity
@Getter
@Setter
@Table
public class DishSize {

    @EmbeddedId
    private DishSizePK id;

    @Column
    private Integer size;

    @ManyToOne(fetch = FetchType.LAZY)
    @MapsId("productId")
    private Product product;

    @ManyToOne(fetch = FetchType.LAZY)
    @MapsId("dishId")
    private Dish dish;

    public DishSize() {}

    public DishSize(Product product, Dish dish, Integer size) {
        this.product = product;
        this.dish = dish;
        this.id = new DishSizePK(product.getId(), dish.getId());
        this.size = size;
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;

        if (o == null || getClass() != o.getClass())
            return false;

        DishSize that = (DishSize) o;
        return Objects.equals(product, that.product) &&
                Objects.equals(dish, that.dish);
    }

    @Override
    public int hashCode() {
        return Objects.hash(product, dish);
    }
}

DishSizePK.java

@Embeddable
@Getter
@Setter
@NoArgsConstructor
@AllArgsConstructor
public class DishSizePK implements Serializable {

    @Column
    private Long productId;

    @Column
    private Long dishId;

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;

        if (o == null || getClass() != o.getClass())
            return false;

        DishSizePK that = (DishSizePK) o;
        return Objects.equals(productId, that.productId) &&
                Objects.equals(dishId, that.dishId);
    }

    @Override
    public int hashCode() {
        return Objects.hash(productId, dishId);
    }
}

Product

@Entity
@Getter
@Setter
@ToString
@Table
public class Product{

    @Id
    @GeneratedValue(strategy = GenerationType.SEQUENCE, generator = "product_generator")
    @SequenceGenerator(name="product_generator", sequenceName = "seq_product", allocationSize = 1)
    private Long id;

    @Column
    private String name;

    @OneToMany(
            mappedBy = "product",
            cascade = CascadeType.ALL,
            orphanRemoval = true
    )
    List<DishSize> dishSizes = new ArrayList<>();

    public void addDish(Dish dish, Integer size) {
        DishSize dishSize = new DishSize(this,dish,size);
        dishSizes.add(dishSize);
        dish.getDishSizes().add(dishSize);
    }

    public void removeDish(Dish dish) {
        for (Iterator<DishSize> iterator = dishSizes.iterator(); iterator.hasNext(); ) {
            DishSize dishSize = iterator.next();

            if (dishSize.getProduct().equals(this) &&
                    dishSize.getDish().equals(dish)) {
                iterator.remove();
                dishSize.getDish().getDishSizes().remove(dishSize);
                dishSize.setProduct(null);
                dishSize.setDish(null);
            }
        }
    }

    @Override
    public boolean equals(Object obj) {

        if (this == obj) return true;
        if (obj == null || getClass() != obj.getClass()) return false;

        Product other = (Product) obj;
        return id != null && id.equals(other.getId());
    }

    @Override
    public int hashCode() {
        return Objects.hash(name);
    }
}