Thanks for the links, @MrLittle. I'm checking with our QA/engineering team to see if we made some MIME-type changes recently. If we changed the type for PDF files it could make the browser think it's just a file and download it.
Our QA team took it to our engineers to fix, although I'm not sure how long that will take. Thanks for your patience!
I also have a website with weebly (mrlama.weebly.com) and have noticed the exact same issue that Mr.Little experiences. All of the pdf files on my weebly website used to open up automatically within the browser when you clicked them. Only recently, I have noticed that now when I click on a pdf file, it immediately asks to download the file. I also did not make any changes to my website for this to happen and am very interested to see what the engineering team will find to help up. Thank you Mr. Little for bringing up this issue. And thank you Adam for trying to resolve the problem. Looking forward to hear your response.