Consider Chrome, automatically, by default, replicates all your passwords to all your devices on which you are signed in.
Thankyouverymuch. I am gonna keep using my password book.
There is no sure way, as a private person and not being expert in security, to secure your browser. But there are ways to limit the damage that can be made. Maybe just don't make it too convenient and have a database of all your passwords on all your devices?