There are really two parts to this. The first is philosophical. The concern about the validity of using instruments to make measurements is an extension of the debate between realism and insturmentalism. That is quite a large topic, subject to its own SEP article.
The actual question, however, is one for metrology. Metrology is the study of measurement, and thus is very interested in the calibration of scientific instruments. The hallmark of a formally tested scientific instrument is extremely consistent results. Measuring the same thing multiple times should give the same results (within some error bound, which metrology quantifies). Measuring two correlated quantities (such as the mass of 500 carob seeds and 1000 carob seeds) should yield correlated measurements. Measurments done in different environments should yield the same results. And finally, measurements done by different people should yield the same results.
How we go about formally verifying that is a very large topic. For small scale efforts, it may be as simple as having a "calibration object" such as an object known to have a mass of 100g. This can be used to ensure the device has the expected reading at one point. For more important measurements, one may send the device to a metrologist to be calibrated. They may test it in multiple ways to get a better sense of how the device measures across a range of values. This often results in a certificate stating when, where, and by whom the calibration was done.
At higher levels, the process gets more refined and more unique. Consider the example of the kilogram prototypes. There was one official object with a mass defined to be 1kg, sitting in a vault in France, known as the IPK. Its mass was, until 2019, defined to be 1kg, so no measurement was needed to know what its mass was. It has 6 "sisters," K1, 7, 8(41), 32, 43 and 47 which are stored in the same vault. These hardly ever see the light of day. There are then 10 "working" copies used in calibration efforts. Beyond that, there are the "national" copies which are held in various nations (K20 is held in the USA).
On occasion, these national copies are calibrated against the working copies. The working copies are calibrated against the IPK's sisters. And every now and then, the IPK itself is actually pulled from its triple bell jar and used to calibrate everything. These measurements must be extremely consistent or they will not be accepted. If a measurement was way out of line with the expectations, the particular instrument doing the measuring will be questioned, and more measurements will be done to achieve consistency.
Interestingly enough, there is some drift. The replicas have, on average, gained 25ug (which means the mass of the IPK has gone down, the mass of the replicas have gone up, or some combination of the two). Dealing with that frustration takes us to one of the highest levels of rigor a scientific instrument will undertake: comparisons with other methods.
In 2019, the kilogram was fixed based on universal constants, rather than a physical object. There were actually several separate efforts to define the kilogram in this way. The most famous are those of the Kibble Balance, balancing mass, voltage, and current, and the efforts of the Avagadro Project, which sought to balance mass and avagadro's constant (a count of how many atoms there are in an object). These approaches were completely unrelated. The kilogram was fixed in 2019, mostly in response to these two methods yielding consistent results out to 8 digits. This was a more consistent pair of values than the measurements of the IPK itself were, so we blessed them as "the kilogram."
(The redefinition of the kilogram chose the Kibble balance approach, fixing Plank's Constant. I have not fully researched why this was chosen over the Avagadro Project's approach, but my suspicions are that the Kibble Balance was deemed easier to reproduce and achieve consistent results with. The Avagadro Project was quite dependent on the extraordinary skills of one single optician who could craft the silicon spheres they need to the precision they need.)