Safe, Efficient Automobile Travel to Better Ensure Lives in Transit (SEATBELT) Act of 2003 - Amends Federal highway law to direct the Secretary of Transportation to: (1) make a two-year grant to each State that has in effect a primary enforcement safety belt use law; and (2) carry out a program for making safety belt usage award grants to eligible States. States as purposes of the latter grant program to: (1) increase the national seat belt usage percentage; and (2) reward States that maintain a seat belt usage rate above 85 percent or demonstrate an increase in such rate.