1) Become more important 2) Increase 
• (v. i.) To become large; to dilate. • (v. t.) To make great; to aggrandize; to cause to increase in size; to expand.
Great'en intransitive verb To become large; to dilate. [ R.] « My blue eyes greatening in the looking- glass.» Mrs. Browning. Great'en transitive verb To make great; to aggrandize; to cause to increase in size; to expand. [ R.] « A minister's [ business] is to greaten and exalt [ his king].» Ken.