The fact that access and excess resemble each other as words is because of a family resemblance they brought to English from Latin, their shared language of origin. They also came into English at the same time, in the 14th century, a period when the French used by the ruling classes in England was contributing new words to English vocabulary, and the educated people of the time often also had a knowledge of Latin that influenced the early uses of these words.
Meaning and Usage of 'Access'
This combination of influences is evident in the oldest meaning of access in English, a meaning that today is much more common in French: “an attack or onset of illness or disease.” This was one of the word’s meanings taken from the Latin word accessus: “onset (of fever or illness).”
Our more common and more general meanings of access, however, descend from the other meanings of accessus derived from the ultimate Latin root, the verb accēdere, meaning "to approach." This gave the Latin noun the meanings “approach,” “means of entry,” and “right of approach.” Our modern word retains all of these meanings.
One can see the link between the word's earliest use, meaning “beginning,” or, figuratively, “opening,” and a literal opening—something that gives access. By Shakespeare’s time, this was by far the most common use of the word, in phrases like “denied access” or “free access.”
The use relating to connectivity to networks or the internet, “freedom or ability to obtain or make use of something,” dates to the late 1950s, as does the corresponding verb use, which was initially regarded as computer jargon but has become so common since the 1990s as to be unremarkable. Its use now even goes beyond tech contexts:
access the internet
access information
access funds
access memories
The use of access as a verb became established in many of our lifetimes, but it’s not criticized as so many recent usages are, probably because of its utility and ubiquity, as well as the word’s familiarity as a noun. Sometimes languages make big changes that are hardly noticed.
Meaning and Usage of 'Excess'
Excess comes from the Latin noun excessus meaning “departure” or “projection,” and ultimately from excedere, the verb meaning “to exceed.”
“Exceeding” brings the idea of “too much,” and to the neutral use of excess (meaning “an amount more than needed”) another meaning was almost immediately added, giving the word a moral component, or a connotation that this was a bad thing. This sense is what Samuel Johnson referred to as “faulty superfluity” and Noah Webster called, more simply, “indulgence.”
As night follows day, what happened was a return of the excesses of the 1920s.
— Huffington Post, 31 March 2011
Excess is most often encountered as a noun or adjective, but there is also a rare verb use of excess, meaning “to eliminate the position of,” a usage that is redolent of the impersonal bureaucratic business jargon that people seem to love to hate. It’s also found in legal contexts. Unsurprisingly, it’s a very recent development, first recorded around 1970.
It should be noted that a preferred list for a particular title or position is a "moving target" as names are added to it to reflect the reinstatement rights of individuals excessed as the result of subsequent layoffs.
— New York Public Personnel Law, 28 March 2019
Overlap Between 'Access' and 'Excess'
The coincidence of the resemblance of spelling and sound of the words excess and access sometimes leads to their confusion today. But, if they seem to intersect in usage—what would be called an error by most editors and teachers—it turns out that, according to the Oxford English Dictionary, these words have been confused from the very beginning, and at the very least a slight overlap in meaning was present at the origin of the use of these words in English in the late 1300s.
That original meaning of access, “attack” or “onset of a disease,” was very nearly the same meaning as the oldest, now obsolete, use of excess in phrases like “excess of mind” or “excess of soul,” referring to a “trance” or the attack or onset of an unusual or unnatural state of mind, sometimes a kind of prayerful ecstasy.
Indeed, in the famous Middle English translation of the Bible known as the “Wycliffe’s Bible,” two different passages seem to use the words interchangeably:
excess of my soule
axcess of soule
One could almost interpret these uses using more modern distinctions: an “access” or attack could come from an “excess” of feelings or emotions. The fact is, in a period without universal literacy, standard spellings, or (gasp) dictionaries, words that resembled each other were often used interchangeably by different writers, translators, editors, or printers.
To summarize their usage, then: access can be used as a noun:
access to beaches
wheelchair access
internet access
Or as a verb:
access my email
While excess is commonly used either as a noun:
an excess of 10 gallons
excess of sugar
the worst excesses of greed
Or as an adjective:
excess baggage
Or, you might just say that this article provides access to an excess of information.