Postgres: "cumulative" view of table

I have a table of changes like this

CREATE TABLE IF NOT EXISTS changes (
    entity_id TEXT NOT NULL,
    column_id TEXT NOT NULL,
    value JSONB NOT NULL,
    updated_at TIMESTAMP NOT NULL
);

INSERT INTO changes VALUES ('1', 'height', to_jsonb(140), '01-01-2021 00:00:00'::TIMESTAMP);
INSERT INTO changes VALUES ('1', 'weight', to_jsonb(30), '01-01-2021 00:00:00'::TIMESTAMP);
INSERT INTO changes VALUES ('1', 'height', to_jsonb(145), '01-02-2021 00:00:00'::TIMESTAMP);
INSERT INTO changes VALUES ('1', 'weight', to_jsonb(34),'01-03-2021 00:00:00'::TIMESTAMP);


 entity_id | column_id | value |     updated_at      
-----------+-----------+-------+---------------------
 1         | height    | 140   | 2021-01-01 00:00:00
 1         | weight    | 30    | 2021-01-01 00:00:00
 1         | height    | 145   | 2021-01-02 00:00:00
 1         | weight    | 34    | 2021-01-03 00:00:00

And I want to get kinda cumulative view of this table

entity_id  | height | weight |     updated_at      
-----------+--------+--------+---------------------
 1         | 140    | 30     | 2021-01-01 00:00:00
 1         | 145    | 30     | 2021-01-02 00:00:00
 1         | 145    | 34     | 2021-01-03 00:00:00

My current query looks working

SELECT
  entity_id,
  coalesce(change->'height', lag(change->'height', 1, null) over (partition by entity_id order by updated_at)) as height,
  coalesce(change->'weight', lag(change->'weight', 1, null) over (partition by entity_id order by updated_at)) as weight,
  updated_at
FROM (
    SELECT entity_id, json_object_agg(column_id, value) as change, updated_at FROM changes
    GROUP BY entity_id, updated_at
) as changes;

But I don't like json_object_agg here and I'm sure there is a way do it without redundant aggregations? some kind of using window aggregate function that I've missed.

UPD. @SelVazi helped to make query better, but I feel it's not the final solution.

with cte as (
  SELECT
    entity_id,
    max(case when column_id = 'height' then value::int end) as height,
    max(case when column_id = 'weight' then value::int end) as weight,
    updated_at
  from changes
  GROUP by entity_id, updated_at
)
select
  entity_id,
  coalesce(height, lag(height) over (partition by entity_id order by updated_at)) as height,
  coalesce(weight, lag(weight) over (partition by entity_id order by updated_at)) as weight,
  updated_at
from cte;

This is more complicated that it may seem. Pivoting the height and weight to columns can be done with conditional aggregation, but then we have to fill the "missing" values.

I would assume that there could be gaps of more than one date for any of the two measures, which makes lag() the wrong fit in Postgres, since it can only look back over a predefined number of rows (and cannot ignore null values).

We can demonstrate the problem with lag() by adding just one row at the end of your sample data:

One workaround uses a gaps-and-islands technique to put "missing" values in groups that start with a non-null value, which then becomes the new value.

select entity_id, updated_at,
    max(height) over(partition by entity_id, grp_height) height,
    max(weight) over(partition by entity_id, grp_weight) weight
from (
    select c.*,
        count(height) over (partition by entity_id order by updated_at) grp_height,
        count(weight) over (partition by entity_id order by updated_at) grp_weight
    from (
        select entity_id, updated_at,
            max(value::text) filter(where column_id = 'height') height,
            max(value::text) filter(where column_id = 'weight') weight
        from changes
        group by entity_id, updated_at
    ) c
) c
order by entity_id, updated_at

fiddle

Instead of using json_object_agg you can use the conditional aggregation to get hight and width as columns :

SELECT entity_id, MAX(CASE WHEN column_id = 'height' THEN value::text END) AS height
                , MAX(CASE WHEN column_id = 'weight' THEN value::text END) AS weight
                , updated_at
FROM changes
GROUP BY entity_id, updated_at

The final query :

SELECT
  entity_id,
  coalesce(height, lag(height, 1, null) over (partition by entity_id order by updated_at)) as height,
  coalesce(weight, lag(weight, 1, null) over (partition by entity_id order by updated_at)) as weight,
  updated_at
FROM (
    SELECT entity_id, MAX(CASE WHEN column_id = 'height' THEN value::text END) AS height
                , MAX(CASE WHEN column_id = 'weight' THEN value::text END) AS weight
                , updated_at
    FROM changes
    GROUP BY entity_id, updated_at
) as changes;

Result :

entity_id	height	weight	updated_at
1	        140	    30	    2021-01-01 00:00:00
1	        145	    30	    2021-02-01 00:00:00
1	        145	    34	    2021-03-01 00:00:00