Leigh
The only attachment I can see is a shot of the export settings. Did you intend to also upload a screen shot of the photo?
To pick up Glenn's point, as I understand it, there are important differences between the working colour space and the output colour space. Some software programs will default to unusual or even proprietary colour spaces for the purposes of editing raw files, with a view to maximising the sublety of colour adjustments and the gamut of colours available. However, as Glenn says it is important particularly for web viewing to ensure the output is in sRGB. Whether you need to select this in export settings will depend on software, I expect, and I also would have thought that the act of exporting into a JPEG forces a file to convert into a sRGB colour space (I'm assuming the default colour space for JPEG is sRGB) but I may be wrong. You would not be able to upload a JPEG to BLP if it were not in sRGB, I think.
Regardless, the software should be exporting the file in a way which achieves a JPEG that is as close as possible to what is seen on your screen during raw editing, whatever working colour space you are using. Some changes are possible in the exporting process (eg sharpening, noise reduction) but as long as you are not compressing the JPEG excessively, comparing the exported file with the edited picture in your raw processing software on the same screen should not show dramatic differences in brightness, I would have thought. If this were the case, it would be impossible to produce good JPEG images, as some guesswork about the export process settings would always be involved.
Our website uses standard web software which I would expect displays JPEG images exactly as they are uploaded. In other words, as far as I know it does not edit any aspects of the JPEG file, including the colour and brightness values. Viewing the JPEG file in a browser vs using windows photo viewer should not show significant differences. As I am sitting here at the computer, I have a recent image of mine open on the BLP web page in two different browsers, as well as the original JPEG I uploaded to BLP open in the windows photo viewer, and all are identical in brightness and colour viewed at 100% size on the same screen. So I'm not sure what is happening to make you perceive an image as brighter on the web than in other software on your computer. Our web site does not add brightness, nor should your browser be adding brightness.
I think it's important that you are comparing apples with apples. You should probably not be comparing a JPEG open in a software program which does not use sRGB as its working space, with a JPEG viewed in a web browser. It is quite possible that your software program might be doing some strange things to the JPEG to bring it back into its own colour space, resulting in a slightly different appearance in your monitor.
One common source for too bright output images is that the monitor brightness is not set correctly for the workspace. As a result, the photographer may increase the overall brightness of an image in the software to compensate, resulting in an image that looks overly bright on another monitor which has been properly calibrated. To achieve accurate brightness and colour, ideally at least the monitor you use as your primary editing tool should be calibrated using a suitable tool, although I appreciate this may not be possible. These tools can also help you set brightness levels of your monitor appropriate for your working environment, such that you are getting a consistent approach (in my experience the setting will often look too bright in a dimly lit room, leading to a desire to turn down brightness to sub-optimal levels). It is also important to pay attention to the histogram during editing, which will give some indication of the brightness of the image independent of the monitor although it's not foolproof. You could also use the eyedropper tool to measure the colour values of white areas of the image; which should be close to clipping but not actually clipped. One other trick I sometimes use is to view images on a device which has screen brightness which responds to ambient light levels (in my case, and iPad Air). iPads in particular have quite good colour and brightness management at default settings, so if a picture looks OK on them in normal room lighting, it should look OK on most other screens.
Thanks
Simon