Currently in Texas, possession of up to 2 ounces of marijuana is a Class B misdemeanor, which can be punishable by up to 180 days in jail and a $2,000 fine. House Bill 441, authored by state Rep. Erin Zwiener, D-Driftwood, would reduce possession of 1 ounce or less to a Class C misdemeanor, which carries no jail time.Apr 29, 2021