Thank you to davidfetter_disq for helping me reach this conclusion. Thank you as well to johto and ASnyder for offering their help :)

final_query.sql

WITH my_vars(intensity_2_duration, intensity_3_duration) AS (VALUES 
  (
    (SELECT (SUM(duration)*2) FROM users INNER JOIN workouts ON workouts.user_id = users.id
      WHERE intensity = 3 AND workouts.deleted_at IS NULL),
    (SELECT SUM(duration) FROM users INNER JOIN workouts ON workouts.user_id = users.id
      WHERE intensity = 2 AND workouts.deleted_at IS NULL)
    )
)
SELECT MAX(date), (SELECT (intensity_2_duration + intensity_3_duration) FROM my_vars) as total_duration, SUM(duration)
FROM workouts
INNER JOIN users on users.id = workouts.user_id
WHERE workouts.deleted_at IS NULL;

gistfile1.txt

I'd like to create a query which selects all of the workouts that belong to a user, which collects the SUM of the duration for each given intensity - adds a multiplier based on the intensity integer, and then returns a single result.

That's a weird way to put it - some pseudocode is below:

SELECT SUM(intensity_2_duration + intensity_3_duration), workout_date
FROM workouts
inner join users
  on user_id = users.id;

Where intensity_2_duration & intensity_3_duration would be represented as something like

SELECT SUM(duration * 50), workout_date
FROM workouts
inner join users
  on user_id = users.id;

oddity.sql

WITH my_vars(intensity_2_duration, intensity_3_duration) AS (VALUES 
  (
    (SELECT (SUM(duration)*2) as intensity_3_duration
      FROM users 
      INNER JOIN workouts 
        ON workouts.user_id = users.id
      WHERE 
        workouts.intensity = 2
        AND 
        workouts.deleted_at IS NULL
        AND
        workouts.date > now()::date - interval '1 weeks'
        AND
        users.id = 3),
    (SELECT (SUM(duration)) as intensity_2_duration
      FROM users 
      INNER JOIN workouts 
        ON workouts.user_id = users.id
      WHERE 
        workouts.intensity = 3 
        AND 
        workouts.deleted_at IS NULL
        AND
        workouts.date > now()::date - interval '1 weeks'
        AND
        users.id = 3)
    )
)
SELECT MAX(date), (SELECT (COALESCE(intensity_2_duration,0) + COALESCE(intensity_3_duration, 0)) FROM my_vars) as total_duration, SUM(duration)
FROM workouts
INNER JOIN users on users.id = workouts.user_id
WHERE 
  workouts.deleted_at IS NULL 
  AND workouts.date > now()::date - interval '1 weeks'
  AND workouts.user_id = 3;

workouts_table.sql

Workouts
-------------
user_id (integer)
intensity (integer)
duration (integer)