What exactly do you mean with tube fittings? Do you mean orbital welded tubing fittings? Since you're referring to butt-weld type Im assuming youre not looking for compression type fittings (e.g. Swagelok). ASME BPE defines butt weld type fittings which has dimensions that are in the tube range. Apart from that Im not aware of any other standard which does the same for tubing fittings. For simplicity Im assuming tubing goes up to 1".
Also, keep in mind B16.9 specifies, in general, main fitting dimensions for piping according B36.10/.19. ASME B16.25 specifies dimensions for welding ends based on various OD and wall thickness combinations.