nice to see you around Jarvis

Spot on, Alexandre. You want your pixel dimensions to always be combination of 16, 32, 64, 128, 256, 512, and/or 1024. (Power of 2 rule, I read somewhere). If you're doing a flat color for example on a wall, you could do a 32x32 square instead of doing a honking 512x 512, since detail isn't an issue. For pictures to go on walls, I usually do combinations of 128x256 or vice versa, unless I need to blow it up big and need every bit of detail. Basically for textures, you want the smallest size you can get and still keep your detail, and always in combinations of those numbers.

Edited to add: if you want to see the difference properly sized textures make in-world, go into your settings panel and change your resolution to medium. Then log out, log back in, and wander around. It's horrifying. I was absolutely appalled when I saw some of my own work in medium the first time I did that.

Resolution is not file size ie; a 2048x2048 texture is not automatically 2Mb in size. I think you have a misconception here.
Depending on the active pixel count and compression/optimizations applied, a 512x512 texture can be 1.25Mb in size, or 300Kb.
It all depends on the content and how it is produced by the designer.
I design in 2048 resolution and often post outfits with shoes at 128, skirts at 256, tops at 512 and faces/hair at 1024 resolutions. Many of my 1024 res textures are in the 140-250Kb range in size after proper post production and optimizations.
When a client sends request for texture, it is compressed by a power of 2, sent to the client computer and placed in it's Utherverse cache. It is not uncommon to see a 2x reduction in file size due to this.
Just wanted to clear this up.

The misconception is yours. Images are NOT compressed when displayed. When stored in video memory images are stored somewhat similarly to BMP format. IOW, the image takes up the same space as a similarly sized, uncompressed BMP. In real terms this means that for every pixel in the image, 3 or 4 bytes of video memory are consumed depending upon whether or not the image has an alpha channel (jpg = 3, png = 4 bytes). Your 2048^2 images will consume either 12MB or 16MB of video memory NO MATTER WHAT SIZE THE FILE IS. The file sizes you mention only affect how quickly they transfer over the network and have absolutely no affect on lag caused by graphics memory being shuffled around.

Now consider this. Assuming the skin of an avatar is jpg format and the avatar is wearing shoes, hair, upper and lower outer garments and upper and lower under garments of type png. If all those images are 2048x2048 that ONE avatar is consuming 132MB of video memory! Even a decent video card with 1GB of memory is going to have problems when you get just a handful of avatars in one property even if all the other textures in that location are minimal.

1024x1024 resolution of those same skin/clothing textures would use only 33MB of video memory. 512^2 images would use 8.25MB. There is no good reason to use textures over 1024x1024 and in the vast majority of cases, no reason to use higher than 512x512.

Using 2048x2048 for any reason just shows a total lack of regard for the gaming experience of others. The choice not only affects the person who purchased and is wearing those textures, but also everyone who is unfortunate enough to be in the same location as them.

That all said, there are file formats that can be used to lesson this impact but UV does not make use of them. Perhaps in the next client...

There are settings one can change in their client. High, Medium and Low. Plus a few others.

Of course if someone uses those to come off of High some stuff is going to start breaking because it was never sized in any of the correct dimensions to start with. Both in Design and Deco.

Actually, I've been noticing that the "Shoulder" issue where a improperly sized outfit would be just on the sholdier is actually fixed. It takes a detail hit and we can tell that the image has a poorer overall quality but yea its fixed.

Same with decorating, seems people complained about it enough and development fixed it. Much to many's irritation and many's cheering, just can't please everyone.