if you are sixteen in massachusetts and you have sex with someone over the age of 18, can the state press charges on the other person?

Yes. The state can press charges.

Chapter 272 Section 4. Inducing person under 18 to have sexual Intercourse.

Whoever induces any person under 18 years of age of chaste life to have unlawful sexual intercourse shall be punished by imprisonment in the state prison for not more than three years or in a jail or house of correction for not more than two and one-half years or by a fine of not more than $1,000 or by both such fine and imprisonment.

“Induce” is defined as: To persuade of influence somebody to do or think something.