I suspect you are assuming accent is only a matter of dynamics, that accent is achieved by loudness. The details of your post all look to me like "how much of the duration of the first beat should I play louder than all the rest."
The problem with that is the accent of beat one is more conceptual that just dynamics. You could play an entire phrase of music with a crescendo without undermining the idea of beat one is accented. Even more emphatically you could have rests on beat one, silence, and still maintain the beat one accent. Rhythmic concepts like syncopation and hemiola also contradict the accented beat one idea. But on "day 4" we don't want to get ahead of ourselves.
The passage of the book describes accent at a very basic level. I don't know how the rest of the book covers the topic, but I assume it doesn't go into issues of beat subdivisions and meter, or else you would not have asked this question.
Re-read that page carefully. The author does not say accent is only achieved by playing a beat strongly. The author does not say beat one is always accented.
I would look at that passage of the book like this. If you had some music which was only quarter notes with no pitch changes (that is essential what the notation shows) the obvious way to play that and achieve some sense of an accented beat one (which would then define a conceptual bar line) is to apply a (dynamic) accent on some of those notes at a regular period.
That book is probably a "fundamentals of music" type text so it isn't going to get into a deep discussion of meter. It just wants to introduce the idea of how to count beats, beat grouping, and the bar line. Do not read it too literally and apply it to performance dynamics.
How are notes weighted if the accent is on first beat?
They are weighted, dynamically accented, any way you like.
This part of the book is not trying to explain that.
I agree with Tim's answer that the onset, the very first moment, of beat one is what is accented. In that sense your example of two quavers on beat one would put a dynamic accent on the first quaver but not the second. I've never read a performance rule of thumb that was so prescriptive. It's just a literal misapplication of a metrical concept to the art of performance.
I think one practical thing should be mentioned about beat one and how its accent is typically and most obviously manifest in music. The accent of beat one is what defines the bar line and two very important things are organized around the bar line: phrase starting and ending, and chord changes. Those are structural elements rather than dynamic elements.
I've started learning music theory and have a question
It's good to have questions and use them to probe a text. But if you're working with Ellul, How to Read Music in 30 Days: Music Theory for Beginners, I would try writing those questions down and set them aside so you can work through the 30 days without getting side tracked. It will be a lot to absorb and you probably want it to flow into your mind unrestricted by questions. At least for that first "30 days." Get it in first, then question it in a second phase. Some questions may be answered within the text but not until you put all the pieces together. Other questions may lead you to other texts. And don't forget that real scores and great performance recordings are often the best textbooks. Look for answers from the great musicians.