Another good answer has already been given to this question, but this answer will address specifically how to see the documents you've referenced in the list of sources attached to your answer.
[Doc. No. 25910, 62 FR 16298, Apr. 4, 1997; Amdt. 61-103, 62 FR 40897,
July 30, 1997; Amdt. 61-104, 63 FR 20286, Apr. 23, 1998; Amdt. 61-110,
69 FR 44865, July 27, 2004; Amdt. 61-124, 74 FR 42549, Aug. 21, 2009;
Amdt. 61-128, 76 FR 54105, Aug. 31, 2011]
"FR" means "Federal Register", and the "Federal Register" is available on-line, at last back through the mid-80's if not much further back. The information in the list includes the page number (16298 in the first item in the list) and the volume number, which you don't really need (62 in the first item in the list).
Let's say I want to check the first source in the list above. Google "Federal Register April 4 1997". Select one of the hits that starts with a url "loc" (Library of Congress) or "gov.info.gov". Use the link to download the April 4 1997 edition of the Federal Register. (Example: https://www.govinfo.gov/content/pkg/FR-1997-04-04/pdf/FR-1997-04-04.pdf ) Go to page 16298. There it is! It is a Final Rule that actually spans pages 16219-16367. You can read all about not only WHAT the FAA changed, but WHY they changed it-- how they justified it in terms of economic costs, safety benefits, etc; what other alternatives were considered, what kind of response they received to their original Notice Of Proposed Rule Making, what was the date of the original Notice of Proposed Rule Making and in which issue of the Federal Register was it published, etc.
Update-- if you read the FARs with this on-line source, the Federal Register references are actually attached to working links-- https://www.law.cornell.edu/cfr/text/14/chapter-I
Also, if you wish to see the FARs as they existed at any given date, here's how to do it--
Go to the government's webpage of cfr's on-line--
In the box on the lower right, browse down to "Title 14" and hit "go"
Browse down to the part you are interested in-- e.g. part 91
There it is--
To see older versions, click on the "Browse/ Search Previous" button in the upper left.
However, it appears you'll only be able to navigate back as far as Jan 1, 2015.
Also, it does not seem to be easy to stay focused on one particular FAR (eg 91.157) as you move around to various dates.
It is also possible to find an on-line ebook of the entire FAR for some years, which you may be able to read for free. Do a "google" search using the "books" option, searching for something like "FAR" or "FAR/AIM", "ebook", and the year of interest.
As far as seeing the revision history of one particular FAR goes, method suggested in the answer starting "Changes to federal aviation regulations are listed on the FAA’s Regulatory & Guidance Library (RGL)" is a good one, but it too is limited in how far back in time you are able to follow the revision history of any given FAR. Certainly, for many regulations, it will not allow you to look back as far as the September 1993 "alphabet reorganization" of the national airspace system. To see further back in time, going directly to the Federal Register is often the best way to go, if you know the date and page number to go to.
The Federal Register may also be searched for NPRM's dealing with a given topic, etc. This is a good way find information about regulatory changes that were proposed, then dropped. "Google" isn't very effective as a search engine for the Federal Register. A temporary subscription to a search engine offered by a company called Hein Online is a better way to go. Some libraries, especially university libraries, may have a subscription that patrons may use.