You are entirely right that much internet information on weapons is fragmentary and contradictory. Part of this is because a lot of the information out there is by enthusiasts of different knowledge levels and there are a lot of old sources and bad scholarship mixed in with good sources and sound methods.

But part of this is because the entire history of weapons and armour is a vast topic and any summary will be fragmentary and contradictory by necessity. Weapons and armour do not exist in a vacuum - they are not simply better or worse than each other, but exist within a tactical, technological and economic context. Weapons do not necessarily fall out of favor because they are inferior - often it is because the manner of war changes. The form of weapons is not just dictated by how efficiently they are shaped for attacking - it is also dictated by how weapons are produced, and the technology available to produce them. We cannot understand weapons and armour without understanding how these factors shaped them. And this is hard, because it requires us to study military history, the history of technology, art history and social/economic history.

All of this is to say that the history of a few weapons or a specific type of armour in a single period is a complicated topic. The history of weapons and armour and the way they interacted throughout history is a massive topic, too big for a single scholar, since it requires too much background knowledge. This is really why historians specialize in general - acquiring in-depth knowledge of a period is itself a full time job - acquiring in-depth knowledge of thousands of years is not possible in a human lifetime. This is why my flair area covers one region and only 350 years.

Zeroing in on the period that I know about, the later Middle Ages in Western Europe, all the factors that I mention mean that the development of weapons and armour is more complex than better weapons driving the creation of better armour. Plate armour was partly, perhaps, a response to crossbows and other weapons, but it was also the product of an increasingly sophisticated steel making process in Medieval Europe - larger blooms from bloomeries could be turned into larger plates (allowing the forcing of large iron plates like breastplates), while waterwheels powered the bellows of the bloomeries and blast furnaces, the drip hammers that pounded the blooms into sheets, and the polishing wheels that polished the finished armour. Similarly the form of swords was dictated not just by their use in battle but also the state of metallurgy - the all-steel one-piece sword blades of the late middle ages could be formed into shapes that would not have been possible in the early Middle Ages. Similarly, we need to place armour and weapons in the context of how they were used - Italian knightly armour and weapons of the 15th century (armour that includes many overlapping and layered plates, a heavy lance, a lance rest mounted high on the breastplate) is well suited to heavy cavalry combat, but not well suited to fighting on foot. As soldiers change how they fight, their tools change to fit the task. Ultimately full plate armour wasn't simply rendered obsolete by stronger and stronger guns, but it stopped -making sense- on the late 16th century battlefield, for a number of reasons. I deal with this more in this answer. In general, the development of armour and weapons in the Middle Ages is not a two-sided arms race of more powerful weapons against stronger armour, but a multi-faceted story involving many causes.

So with that said there are some books to recommend that deal with the development of weapons and armour - heavier on the armour than the weapons.

The Knight and the Blast Furnace by Alan Williams is a history of plate armour in medieval and early modern Europe, as told through its metallurgy. This book deals heavily with the technological developments that made plate armour possible, and looks at how it developed over time. Partially in response to different weapons (mostly firearms), partially as a result of changing industrial processes and economic/social forces. The Sword and the Crucible by the same author deals with swords. Currently I am reading it.

Tobias Capwell's Armour of the English Knight 1400-1450 is a hyper-focused text (the first of two volumes covering only 15th century England) that shows just how the form of armour is developed to suit the purposes it is used for - the way that people fight.

I should point out that all the books mentioned here are massive - folio-sized. Both The Sword and the Crucible and 'Armour of the English Knight' approach 400 pages or exceed it. The Knight and the Blast Furnace is 900 pages long. And there is still so much to be said about these topics.