To cover the legal issue first: I assume the timelines you're talking about focus on the Anglo-American context, so Europe will be my frame of reference here. As codified legal systems grow more complex, thorough, and systematic in the late Middle Ages into the early modern era, one principle develops that is called "coverture" in England but is by no means exclusive to the kingdom. (An even stricter version than the Anglo-American tradition pops up in German cities; on the other hand, Cathryn Spence argues it really didn't have a role in Scotland of all places).

At an extreme, coverture is the reduction of women's legal status to that of children. A woman is "covered" by her closest male relative in the eyes of the law--so, ideally her husband, but this could be a father, brother, etc. if she is a widow or singlewoman. She cannot purchase or discharge property in her own name, cannot represent herself in court (cannot sue or be sued), and cannot make financial/legal transactions without her male guardian's sign-off. Coverture is where the idea that "women can't own property" comes from. All assets and power are nested in the family unit, which is legally controlled by the male head of household. (In contrast, sharia as developing over the Middle Ages holds that wives and husbands bring their own property to the marriage and can earn assets independently).

It is vital to note, however, that the application of coverture to widows and singlewomen was very sporadic. In England, non-married women typically received the status of "feme sole" (as opposed to "feme covert"), which is to say, they could transact business in their own name. This includes the legal aspects associated with property ownership (buying and selling, suing, borrowing and lending, etc). So in some jurisdictions, yes, one might say "women could not own property," but it is generally more accurate to say "married women could not own property independently."

But it bears pointing out that widowhood was the proverbial double-edged sword. While widowhood provided a route to independence, power, and financial succees for some women, letters of petition for aid suggest that it was a burden far more often. (That is, as far as the financial transactions/property ownership aspects of coverture go, the practice difference was nil). There were also often barriers imposed on widows specifically. In many German cities, for example, widows of master craftsmen who inherited their late husbands' shop were legally allowed to own it for 1-2 years, but had to sell or transfer it to another owner after that.

I've discussed the fate of coverture, with some attention to the difference between married and non-married women, in the U.S. in this earlier answer, if you're interested.

In the 15th-16th centuries, which I'll take as the time period under most consideration here, the day-to-day application/enforcement of coverture varied significantly by jurisdiction and time. For a medievalist, a statement like this is a truism, not really needing to be said. For a modern historian, that's probably not so typical to see. This disjunction is key to understanding the second part of your question--did the status of women decline from the late Middle Ages into the early modern era--and why it has spawned such an impassioned scholarly debate.

There is one school of feminist theory that holds, as a broad principle, any codification/systematization of laws, religious practices, education, or other institutions within a patriarchal society is inevitably and necessarily damaging to women. That is, in a world where the "law code" is built off of a pile of precedents, some of which may contradict each other, some of which the individual jurist may not know about in any given time, there is much more room for flexibility in individual cases or applied quite broadly. (There are entire towns in France where no marital law/coverture traces can appear). If there is anything that characterizes the transition from "medieval" to "modern" world, it is codification, systematization, and institutionalization--including of law codes. The development of coverture as a legal principle is often Exhibit A when this school of thought draws on medieval-early modern for evidence (or when scholars of this era are influenced by this version of feminist theory).

Another school of feminist thought points out the problems with grand, sweeping narratives and theoretical principles like coverture. Namely, in actual people's lives, things continued to vary much more than even new laws would suggest. In fifteenth-century Nuremberg, for example, newly widowed Katharina Tucher had to move back to her father's care with her daughter. And yet late in her life, we find her making donations in her own name.

The other major example of "institutionalization, in a patriarchal society, is necessarily worse for women" from the 15th-16th century period involves the rise of urban governments. Specifically, the difference between the increasingly important elected civic governments and traditional landed hereditary nobility. Where officials were elected by varying percentages of the population, laws prohibited women both from voting and from holding office. In some principalities, on the other hand, women could and did rule in their own name as heiresses. But when we consider shifts over time, the question then becomes: how often did women really rule in their own name during the Middle Ages? Is the exclusion of women from power, overall, really all that new? Isn't the only thing that was eliminated, the occasional exception?

Whether the status of women improved or declined from the late Middle Ages into the early modern era is a question that will probably never be settled. Whether that's because Catholics and Protestants once had a massive stake in asserting that the Reformation ruined or saved women, or because feminist historians disagree on the merits of theory, narrative, and general conclusions versus microspecifics and the experiences of each individual, the debate has a long history of its own that will hopefully continue--and continue to produce fascinating research from all camps.