Weir joined Rangers on a short-term deal in January 2007, but has impressed at the club.
“He is showing that he could go again (for another year),” said Smith.
“His experience, professionalism and fitness mean he is able to handle anything thrown at him.
“He has been really steady for us. Our back four, plus goalkeeper Allan McGregor, have defended well this season and Davie has been an integral part of that for more than two seasons now.
“I’ve been pleasantly surprised by him. He keeps going and keeps surprising everybody. But I don’t suppose we should be surprised at what he does anymore.
“He has already surpassed my initial expectations of him at Rangers.
“I thought he would be here for a three or four-month period, from the January until the end of the season, but he is still here and still playing really well.”