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The source is c.1770...

• https://imslp.org/wiki/Scots_Songs_for_Voice_and_Harpsichord_(Bremner%2C_Robert)

...first book.

I can see that the beaming matches the words of the vocal part. But it obscures the beat.

In the second full bar, at the word 'wave' it's a grouping of 3 + 1 eighths. That looks like a triplet on beat 1 and the eighth for "the" on beat 2, but of course it really is 4 eighths in two beats.

Is this beaming normal for vocal parts?

I was trying to sight read from the book, but the rhythm was hard to read. At least for me.

If it's normal vocal practice, I should learn to read it.

If not, I could try to mark over the score in some way.

I really like these folk song settings so I want to figure out how to handle sight reading the score.

It's normal practice for vocal music that went out of fashion in 20th century practice: syllable distribution is now pretty universally indicated by slurs. Among other things, this makes it more straightforward for instruments to double a singing voice. Another is that when syllable distributions differ between stanzas, you can indicate this with a broken slur but changing beaming in a similar manner is much more complicated.

And of course, like you observed, the relation to the beat is easier to see when the beaming follows the meter. All that being said: yes, you'd likely want to get used to this since older editions tended to follow that standard, and older editions often have the advantage of being out of copyright and thus much easier accessible. And urtexts (which some people prefer in new editions as well) follow the manuscript closely and thus would also reflect this practice in case it was in use at that time.

Your example was the standard notation for vocal parts up to about 1950. The beams indicate the notes sung to one syllable of the lyrics. You will find almost all "pre-computer-engraving" vocal scores written that way.

The slurs in your example show exactly the same thing as the beaming, and were sometimes omitted, except over quarter notes or longer which don't have beams.

For long passages (i.e. more than one bar) sung to a single syllable, the beaming followed the normal non-vocal convention, and a slur indicated the extent of the syllable.

In modern notation the beaming follows the same rules as for non-vocal music, and slurs are used to show groups of notes sung to one syllable.

When all music was printed from metal plates engraved by hand, it was no more time-consuming to produce this style of beams. Computer notation software has more or less killed it in favour of beaming all parts the same way, since the old style vocal beaming can't easily be automated.

Singers seem to be divided about which convention is "best" - some find the modern beaming convention hard to read because it hides the rhythmic connection between the words and the music, others (like you) find the old-style rhythms hard to decipher.

Incidentally your example shows another common feature of editions from that period, namely that long notes tend to appear in the middle of their sounding duration, not at the start as in modern music engraving. See the half notes in the first and last bars of the bass line, for example.