You want to be multiplying by the time factor twice - once when converting acceleration to velocity and once when converting velocity to position.
acceleration = force/mass + gravity
velocity += impulse/mass + acceleration * dt
velocity *= drag
position += velocity * dt
The usual thing is to have "dt" be an actual time value in seconds, rather than a scaling factor - that way the acceleration value will be a familiar sort of "spatial units per second per second" value. If you assign "dt" to be 1, that works out the same math-wise but your acceleration value will be in (spatial units per 1/60th of a second) squared.