Papers were indeed read aloud at meetings. This provided an opportunity for discussion afterwards, and transcripts of the discussions sometimes accompany the papers in the various Proceedings journals. Depending on the society, not all of the papers that were read were published in the proceedings; the title and author, or an abstract, was sometimes published when a full papers was not.

The Proceedings of the Royal Society of London typically begins with a summary of the meeting at which the papers were read. For example, volume 46 (1890) begins:

May 2, 1889.

Professor G. G. STOKES, D.C.L., President, in the Chair.

The Presents received were laid on the table, and thanks ordered for them.

...

Professor Georg Friedrich Julius Arthur Auwers, Foreign Member (elected 1879), signed the obligation in the Charter Book and was admitted into the Society.

The following Papers were read :—

followed by the papers themselves.

The papers, despite technical detail, are often written in a quite "chatty" style well-suited for reading aloud. To pick a random example from the above volume [1]:

In the year 1882 I had the honour to lay before the Royal Society a note on the photographic spectrum of this nebula, in which I described a new bright line in the ultra-violet, to which I gave a wave-length of about 3730. In addition to this new line, the lines of hydrogen, Hβ and Hy, which I had discovered by eye in my early observations on the visible spectrum, were to be seen upon the plate.

On account of the faintness of the object the slit had been made rather wide, and for this reason the character of the line and its position, as I stated in the paper, could not be ascertained with the accuracy which I desired.

The modern descendant of this practice is still with us: scientific/academic conferences. A modern conference might or might not include a proceedings volume of full papers, and where they do, at least for scientific conferences, what is printed in the full paper in the proceedings is very rarely what is said in the talk at the conference. In many scientific conferences, the speaker is blessed with 15 or 20 minutes for the talk and Q&A afterwards; this is insufficient for reading a full paper unless one has rather little to say. Thus, the paper provides the valuable service of providing the full details that one doesn't have the time to give in the talk. Whether or not a full paper appears in the proceedings of the conference, the results of the research are often also published in a scientific journal. Where there was a full conference paper, the journal papers is often more detailed and complete.

One interesting case is Proceedings of the National Academy of Sciences of the United States of America (PNAS), which functioned along the lines of a proceedings journal, publishing brief first accounts of research by members of the NAS (regardless of at what conference the member might have talked about the work). In, e.g., physics in the 1970s, there are many examples of a brief paper, essentially what could have been published in the proceedings of a conference, in PNAS, followed by a longer and more detailed paper later in one of the Physical Review journals.

Not all scientific papers were read at meetings. This was the distinction at the time between the Proceedings of the Royal Society of London and the Philosophical Transactions of the Royal Society of Londonat the time (i.e., 1890) - the papers in the Proceedings were read, and the papers in Phil Trans were not. The Phil Trans papers were written in a different style, too. To pick a random example from 1890 [2]:

The object of the experiments described in this paper was to learn how the specific inductive capacity of a dielectric is affected by change of temperature.

...

The present investigation shows an increase of specific inductive capacity with rise of temperature in all the solids examined, and a decrease in all the liquids except one.

As paraffin, which is a substance comparatively near its melting point at ordinary temperatures, shows no change, these results seem to indicate, as far as they go, that the specific inductive capacity of a substance has a maximum value about the melting point. But it may be questioned whether the data are sufficient as yet to warrant so general an induction.

which displays the classic passive voice so stylistically pushed in 20th century scientific writing, rather than the much-decried in the 20th century too-informal "I" of the Proceedings. The evolution of the meeting, reading papers, and publication practices of the Royal Society of London is discussed in [3].

Reading papers word-for-word is not yet extinct. This surprised me when I first encountered it. Scientific conferences typically make generous use of visual aids, with transparencies and overhead projectors last century, and Powerpoint and other computer-projected formats for slides this century, often with animations and video. To go from this type of thing to a conference where the speaker sits down and reads the paper that will appear in the proceedings word-for-word, with no slides or other visual aids was quite a culture shock.

(It's often nice when a speaker brings something in for show-and-tell, such as a box of beetles, or some boomerangs, or whatever. This kind of thing goes back to at least the 19th century [4].)

References:

[1] William Huggins and Margaret Lindsay Huggins, 1890, "On the spectrum, visible and photographic, of the Great Nebula in Orion", Proc. R. Soc. Lond. 46, 40-60, http://doi.org/10.1098/rspl.1889.0005

[2] W. Cassie, 1890, "On the effect of temperature on the specific inductive capacity of a dielectric", Philosophical Transactions of the Royal Society of London 181, 1-17, https://doi.org/10.1098/rsta.1890.0001

[3] Aileen Fyfe and Noah Moxham, 2016, "Making public ahead of print: Meetings and publications at the Royal Society, 1752-1892", Notes Rec. 70, 361-379, http://doi.org/10.1098/rsnr.2016.0030

[4] Juliana Adelman, Communities of Science in Nineteenth-Century Ireland, Routledge, 2015, pg 27.