While I agree with Wai-keung as far as his reply goes, it depends somewhat on the rapidity with which you expect the differences to occur between individual cuts !
If you expect a significant difference between each of the cuts, then the five-sample average may eliminate the differences largely, leading to erroneous information.
However, if the cut-to-cut variations are slow (or detectable after every say, hundred samples), then the averaging may not have much of a filtering effect.
(This in a nutshell, is what Wai-keung implies by low pass filtered data.)
If you are uncertain about the above, using all the samples will always give you an accurate (though perhaps a bit laborious !) picture.
You will obtain the same average weight for both methods. However, method 1 will also give you a better idea of the inter cut variation in the form of standard deviation or inter-quartile range.
The more data points you have the more information you can extract from the process.