How to subtract next row from first one for each account id in SQL?

The question I am trying to answer is how can I return the correct order and sequence of weeks for each ID? For example, while it is true the first week for each ID will always start at 1 (its the first week in the series), it could be the following date in the series may also be within the first week (e.g., so should return 1 again) or perhaps be a date that falls in the 3rd week (e.g., so should return 3).

The code I've written so far is:

select distinct 
row_number() over (partition by ID group by date) row_nums
,ID
,date 
from table_a

Which simply returns the running tally of dates by ID, and doesn't take into account what week number that date falls in.

But what I'm looking for is this:

Here's some setup code to assist:

CREATE TABLE random_table

  (
  ID VarChar(50),
date DATETIME
 );

 INSERT INTO random_table
 VALUES
  ('AAA',5/14/2021),
('AAA',6/2/2021),
('AAA',7/9/2021),
('BBB', 5/25/2021),
('CCC', 12/2/2020),
('CCC',12/6/2020),
('CCC',12/10/2020),
('CCC',12/14/2020),
('CCC',12/18/2020),
('CCC',12/22/2020),
('CCC',12/26/2020),
('CCC',12/30/2020),
('CCC',1/3/2021),
('DDD',1/7/2021),
('DDD',1/11/2021)

with adj as (
    select *, dateadd(day, -1, "date") as adj_dt
    from table_a
)
select
    datediff(week,
        min(adj_dt) over (partition by id),
        adj_dt) + 1 as week_logic,
    id, "date"
from adj

This assumes that your idea of weeks corresponds with @@datefirst set as Sunday. For a Sunday to Saturday definition you would find 12/06/2020 and 12/10/2020 in the same week, so presumably you want something like a Monday start instead (which also seems to line up with the numbering for 12/02/2020, 12/14/2020 and 12/18/2020.) I'm compensating by sliding backward a day in the weeks calculation. That step could be handled inline without a CTE but perhaps it illustrates the approach more clearly.