Nitpick, weight and mass are fundamentally the same thing due to the Einstein equivalence principle. The defined way of measuring them may be slightly different but they measure the same fundamental property. As they are defined mass is a measure of the energy required to move an object and weight is the observed force of an object being accelerated due to gravity which is the same fundamental force in this universe.
Second note that while the change may be harder to observe the changes in mass due to the relative small numbers but it is not constant either. As an example, if you are measuring the mass of a clock it will have more mass when it is running than when it is stopped.
Third note, the avoirdupois ounce is defined as exactly 28.349523125 g, and thus is based off the prototype kilogram so they are just different scales of the same exact measure.