Differences can appear in multicolumn indexes because two ints takes 8 bytes while two bigints takes 16, however the right layout of columns for an index is not always the layout that minimizes padding.
CREATE TABLE foo
(id INT GENERATED ALWAYS AS IDENTITY PRIMARY KEY, iid INT NOT NULL);
CREATE TABLE bar
(id INT GENERATED ALWAYS AS IDENTITY PRIMARY KEY, iid BIGINT NOT NULL);
CREATE TABLE baz
(id BIGINT GENERATED ALWAYS AS IDENTITY PRIMARY KEY, iid BIGINT NOT NULL);
-- fill each with 1,000,000 rows, then index
CREATE INDEX {foo,bar,baz}_iid_idx ON {foo,bar,baz}(iid);
SELECT table_name,
pg_size_pretty(pg_table_size(quote_ident(table_name))) "table_size",
pg_size_pretty(pg_indexes_size(quote_ident(table_name))) "index_size"
FROM information_schema.tables
WHERE table_schema = 'public';
table_name | table_size | index_size
------------+------------+------------
foo | 35 MB | 43 MB
bar | 42 MB | 43 MB
baz | 42 MB | 43 MB
As your example shows, there is no benefit in index size (e.g for supporting FKs) in going from int to bigint for a single key. You end up with the same index size no matter what, not twice the size which was what I took your original post to mean.