Not really sure about how your gallery looks because it never loaded from the URL in your post, and I don't know if that's a javascript issue or what--but I'll take a stab at helping you come up with a solution. Image optimization is image optimization, regardless of whether or not you're building a responsive site.
Approach and Design Considerations
Do you really need one large, high resolution image for each item, at the same DPI/PPI and compression, that should be responsive?
Or, should you serve appropriately sized images at differing DPI/PPI and compression, to different displays, all of which are still used in a responsive application?
Popular Convention
You're showing a gallery, and typically, you want smaller representations of the actual image--thumbnails or placeholders, generally of lower resolution, which link to the actual image at a higher resolution. This is an accepted design approach, and if you're going to vary from it, be sure it's with good reason.
The Lowest Common Denominator
If you're building a responsive site, some users will obviously be on mobile devices which may have resolutions as small as 320 pixels wide. Consider things like that, and this: even if someone shows up on a desktop, are you going to have huge, full width images loading? They will take forever to load, and visitors will never see your gallery. How is your gallery to look on a wide screen desktop? If your intention is to have one image full width across the entire page, and load the same image regardless of the device accessing your site, you may be using responsive design, but you'll find that's far away from best or even good practice.
The Flip-Side, Large/Wide Screens
Why not have four gallery images going across a desktop? Or more? And if that's the case, they're likely to have a maximum size in any case. I honestly don't know because I've tried to load your site a few times and get nothing. But consider that if there's a maximum size practically for your gallery images in an initial display, say 6 images at 200 pixels each across a 1200 pixel max layout width (Or, are you using a % based framework and using 100% of the display width? Even responsive sites often limit the max width of the content area, and these things all would help determining a more appropriate answer) solutions begin to emerge.
Since no image needs to be larger than 200 pixels in that case, and on a phone where your columns might be displaying only one image that you want full width, you can work with a maximum initial width of 480px wide images.
Higher Quality, Smaller Files
We'll assume you want them high quality. That's fine. You still need to reduce files size, and you do that with compression. Now, you may feel compressing a photo to 50% or even more makes it blurry, and it certainly will at low ppi (pixels per inch) settings.
The Secret To Better Compression
What you need to do is change default image editor settings from traditional defaults like 72 or 90 ppi, and crank them up to 300, 400, 500, or more--and THEN apply compression. If that image is 480px wide, and you've only got 72ppi, compression will quickly erode quality. However, having several hundred extra pixels per inch will allow more information to be stored. Then, you can apply much higher compression rates, and shrink file sizes down quite a bit more.
The Oversized Image Approach
Another trick is to do the same thing, and slightly oversize the image. If 480px is the max size for your thumbnails/small pics, make them actually 540-600 px wide, with 400-500ppi and compress them at really high settings. The browser will resize to the max width of 480 px...but then you have a performance hit there. Everything is a trade off. You can blur backgrounds in images as well, allowing the foreground/main focus of the photo to be of higher quality while the background requires less information, yielding smaller file sizes.
Not Suitable For Batch Processing
This should be done individually for each image, batch editing does not generally get the most out of this technique, because the color information is so different in each photo. One photo might be best quality and smallest size for your purposes at 300ppi and 50% quality, another at 500ppi and 35% quality. You'll want to do this not just for your gallery thumbnails, but multiple images. No point in serving up a 1400px wide full size desktop to someone who's browsing your site with 480px wide/resolution display after all. Use media queries to serve up the appropriate ballpark sized image, and have a small, medium and large variant. Done right, you don't even need to be serving larger images to those browsing with phones...the gallery images they are viewing are good enough.
The compression setting is not so heavily determinate of the final image quality as the number of pixels you have to compress goes up. More pixels to work with, the better quality at higher compression settings.
Design Considerations and Smart Image Loading
Break It Up Into Smaller Content Chunks
Also, consider the process/design of your gallery. Do you have 20 items? 100? 400? Are you trying to show them all on one page? Break it up into small numbers...12-20 per page. Smaller and fewer images will load faster, and can remain responsive, with links for those who want a larger or higher quality image. No need to show a huge, high quality image to someone browsing with their phone.
Pre-fetching and Loading
Server side scripting, and even some javascript solutions can help with this. You might do things like limiting each gallery page to four rows of four images, and then after page load, have a javascript that pre-fetches the first four images that will display on page 2. If your visitor goes to page two after scrolling through page one, the first four images are loaded in cache, and display quickly while the others load normally, giving the experience of a faster page load.
If the visitor goes to another page in the site, you didn't waste bandwidth on 12 images and only cost you the bandwidth of four. Smart design might be to use those first four images on page two of the gallery elsewhere on the site...so that first gallery page visit actually sped up page load elsewhere and does not in fact give up bandwidth for loading 4 unnecessary images. Think the process through, and solutions will suggest themselves.
Resources
Anyway, here are relevant articles/posts/links you may find helpful in understanding all of this:
Are Compressive Images A Good Solution For High Resolution Displays?
http://www.vanseodesign.com/web-design/compressive-image-tests/
Reducing image sizes (ResponsiveDesign.is)
https://responsivedesign.is/articles/reducing-image-sizes
Search benfrain dot com for this post:
How to serve high-resolution website images for retina displays
And a tool you might find useful...
adaptive-images dot com