In a StackOverflow answer, I attempted to explain why a 32-bit float was perfectly adequate for representing the questioner's weight measurement:
Physical properties are inaccurately measured anyway:
no measuring instrument is perfectly calibrated or completely reliable (e.g. weighing scales cannot adjust for the exact gravitational field at the precise time and place in which they are used, or may have undetected mechanical/electrical faults); and
no measuring instrument has infinite precision—results are actually given across some interval, but for convenience we often adopt a "shorthand" representation in which that information is dropped in favour of a single number.
Consequently, all that anyone can ever say about a physical property is that we have a certain degree of confidence that its true value lies within a certain interval: so, whereas your question gives an example weight of "5 lbs 6.2 oz", what you will actually have is something about which you're, say, 99.9% confident that its weight lies between 5 lbs 6.15 oz and 5 lbs 6.25 oz.
Seen in this context, the approximations of a 32-bit float don't become even slightly significant until one requires extraordinarily high accuracy (relative to the scale of one's values). We're talking the sort of accuracy demanded by astronomers and nuclear physicists.
But something about this has been bugging me and I can't quite put my finger on what it is. I know that it's completely unimportant for the purposes of that StackOverflow answer, but I am curious:
Is what I have said (about errors and uncertainty in measuring physical properties) completely, pedantically correct?
I acknowledge that knowing the gravitational field is only relevant if one wishes to ascertain a body's mass, however at the time it struck me as a good illustration of experimental errors: systematic error from "imperfect calibration" (i.e. to the gravitational field at the scales' location of use) and random error from the instrument's "unreliability" (i.e. fluctuations in the field over time).
Is there is a similarly simple and accessible illustration of error that is more relevant to weight? Perhaps the inability to perfectly calibrate springs, together with the randomness of their precise behaviour due to quantum effects? (If that's not complete and utter nonsense, then I'm truly amazed!)
Have I omitted any further points that would help to justify my conclusion (that a 32-bit float is adequate for the OP's needs)?
Perhaps I have not fully explained the types or risks of experimental error? Perhaps I have not fully explained the limitations of physical measurements?
The final sentence quoted above (re astronomers and nuclear physicists) is, of course, an exaggeration: is there a better analogy?
I decided to remove from my original answer this rant about physical measurement, since it was pretty tangental to the purpose of that question. Nevertheless, I am curious to find a good answer to this question.