Weld "clean" on a frame. Weld 'into' the 3/8" - to: the 1/8 so you don't notch the frame and create a brittle HAZ.that could eventually crack out from stresse(s). What kind of load (if any) will the added 3/8"+ the weld have to handle? Also take care not to distort the frame (if applicable) from over-doing it.