2) Arthur was a leittle boy but he... swim better than

1) Arthur was a little boy but he could swim better than me.

2)Take a sweater with you, Ann. It may get colder later", the mother said.

 Some verbs are called modal verbs. Modal verbs are may, must, can.

We dont use to before modal verbs. We dont use to after modal verbs. We dont add suffixes to modal verbs.

Could is the past form of can.

Might is the past form of may.

We can use have to insist of must. Must takes had to in the past.

The first sentence is in Past Indefinite. Thats why we use could.