Images much larger on server and page than the local version
This is likely to be a combination of factors.

Firstly; GD isn't all that great, so if you can get ImageMagik installed it's possible you'll get better results.

Secondly; This can depend on the image format too. PNGs for example are far more complicated to save optimised and it's unlikely that a PNG generated by a server is going to match the level of optimisations you can get locally through tools like TinyPNG and ImageOptim. PNGs have many more options for quality control than JPG's simple slider. Try to avoid transforms on anything other than JPGs.

Thirdly; check you're uploading an image that's larger than the crop you're creating. Craft has a horrible behaviour of blowing up images to match the crop. It's not really cropping, it's just taking any image and making it the size requested. That can mean 'cropped' images larger in filesize and dimension than the source.