public class Month()
{
    public int ID { get; set; }
    public string Name { get; set; }
    public virtual ICollection<Week> Weeks { get; set; }
}

public class Week()
{
    public int ID { get; set; }
    public int MonthID { get; set; }
    public String Name { get; set; }
    public virtual ICollection<Day> Days { get; set; }
}

public class Day()
{
    public int ID { get; set; }
    public String Name { get; set; }
}

public class EditMonthViewModel()
{
    public Month Month { get; set; }
    public List<Week> Weeks { get; set; }
    public List<Day> AllDays { get; set; }
}

@model myProject.ViewModels.EditMonthViewModel

//...
@using (Html.BeginForm())
{
    //Edit Month Stuff...

    @for(int i = 0; i < Model.Weeks.Count(); i++)
    {
        <h2>@Model.Weeks[i].Name</h2>
        @Html.EditorFor(model => Model.Weeks[i].Name)

        //loop through all possible days
        //Select only days that are assigned to Week[i]
        @for(int d = 0; d < Model.AllDays.Count(); d ++)
        {
            //This is the focus of this question.
            //How do you bind the data here?
            <input type="checkbox"
                   name="I have no idea"
                   @Html.Raw(Model.Weeks[i].Days.Contains(Model.AllDays[d]) ? "checked" : "") />
        }
    }
}

public ActionResult Edit(int id)
{
    var viewModel = new EditMonthViewModel();
    viewModel.Month = db.Months.Find(id);
    viewModel.Weeks = db.Weeks.Where(w => w.MonthID == id).ToList();

    viewModel.AllDays = db.Days.ToList();
}

[HttpPost]
public ActionResult Edit(EditMonthViewModel viewModel)
{
    var monthToUpdate = db.Months.Find(viewModel.Month.ID);
    //...

    if(viewModel.Weeks != null)
    {
        foreach (var week in viewModel.Weeks)
        {
            var weekToUpdate = monthToUpdate.Weeks.Single(w => w.ID == week.ID);
            //...

            /*So, I have a collection of weeks that I can grab,
              but how do I know what was selected? My viewModel only has a
              list of AllDays, not the days selected for Week[i]
            */
        }
}

public class DayModel
{
    public int WeekId { get; set; }
    public int DayId { get; set; }
    public bool IsIncluded { get; set; }
}

@{
    var modelIdx = 0;
}

// ...

<input type="hidden" name="days[@modelIdx].WeekId" value="@Model.Weeks[i].Id" />
<input type="hidden" name="days[@modelIdx].DayId" value="@Model.AllDays[d].Id" />
<input type="checkbox" name="days[@modelIdx].IsIncluded" value="@(Model.Weeks[i].Days.Contains(Model.AllDays[d]) ? "checked" : "")" />
@{ modelIdx++; }

[HttpPost]
public ActionResult Edit(IEnumerable<DayModel> days)
{
    //...
}