Consider the following:

    data={{{3544128000, 80}, {3544732800, 80}, {3545337600, 80},
    {3545942400, 80}, {3545942400, 160}, {3546547200, 160}, {3547152000, 0}}};

After the satisfying answers to my former question [(Part 1)][1], another issue occurred, but with the same background (List-operations only when restrictions are fulfilled):

After applying

    Transpose[{#[[All, 1, 1]], 
          Total[#[[All, All, 2]], {2}]}] &[#] & /@ (GatherBy[#, First] & /@
        data)

on `data` (thanks to Andy Ross for the approach), I receive

    {{{3544128000, 80}, {3544732800, 80}, {3545337600, 80}, {3545942400, 240},
    {3546547200, 160}, {3547152000, 0}}}

which resembles to

    {{x_-n*604800_, y_},...,{x_-604800_, y_}, {x_, u_},
    {x+604800_, z_},{x_+2*604800_, z_},...,{x_+m*604800_, z_}}

I would like to do the following:

1. `u_->y_` (*Transform u_ to y_*)
2. `residual=(y_-u_)/(n+1)` (*Calculate residual of y_ and u_ and divide it be `n+1`*)
3. `{{x-n*604800_, y_+residual},...,{x-604800_, y_+residual}, {x_, y_+residual},{x+604800_, z_},{x_+2*604800_, z_},...,{x_+m*604800_, z_}}` (*Distribute `residual` to all periods from `x_-n*604800` to `x_`*)

The result in case of `data` will then be:

    {{{3544128000, 120}, {3544732800, 120}, {3545337600, 120}, {3545942400, 120},
        {3546547200, 160}, {3547152000, 0}}}

For better understanding, please consider the following examples:

    Example1 = {5, 5, 5, 2, 2, 2, 6, 4, 4, 4};
    MyFunction@Example1
    {5, 5, 5, 3, 3, 3, 3, 4, 4, 4}
    
    Example2 = {2, 2, 2, 6, 4, 4, 4};
    MyFunction@Example2
    {3, 3, 3, 3, 4, 4, 4}
    
    Example3 = {2, 2, 2, 4, 4, 4};
    MyFunction@Example3
    {2, 2, 2, 4, 4, 4}

`MyFunction` detects a peak within the dataset and "kills" it by replacing the peak and the preceding sequence (with constant values) with `y+residual` (see `2.`, `Example1` and `Example2`). It is important that `MyFunction` returns the original list when no peak occurs in the list (see Example 3.).

  [1]: https://mathematica.stackexchange.com/questions/4332/list-operations-only-when-restrictions-are-fulfilled-part-1