Never worried about adjusting for added cargo and have never seen it mentioned that you need to worry about checking after the weight.
What is important is to check for proper pressure when the tire is cold. By cold, the manufacturers mean in the morning before the sun shines on the tires and before you have driven 1 mile. If you must drive some place to add air, check the tires and make note of how many pounds you need to add. Drive to where you will add, recheck and add that many pounds to the knew pressure.
Also, DO NOT, I repeat, DO NOT let air out as the pressure rises due to road temps, sun, of driving. The increased pressure is designed into the tire and calculated into the ratings. I have seen 80 psi cold tires go to 110 psi due to driving 200 miles in 110* heat on black well traveled interstate asphalt.