So I made myself a sniper type with light armor and a silenced sniper rifle. However, enemies can spot me from far far away, making it difficult to kill without being seen. How can I make myself stealthier to avoid being spotted so easily?
The problem is that you are behaving in the "standard" stealth way, where you assume that enemies cannot see you if you are fairly far away, in a dark spot. This is how it works in games like Crysis, Deus Ex, or Thief. This is not how EYE stealth works. In EYE, AI perception is based almost entirely on the direction enemies are facing. The AI can see quite a long ways and light is much less important than in other games. While this is more realistic, it is not explained to the player, which leads the player to feel the system is arbitrary or broken. Rather, it is just so abnormal that it demands explanation, which is not provided.
What all this means is that you need to focus almost entirely on a few things for stealth:
Get cloaking, it is going to be needed for when enemies refuse to turn around.
Only use large cover, if its not big enough to cover you you can be seen. This differs from most games where partial cover is enough to hide you.
Peek out very carefully, exposing minimal body in order to see which direction enemies are facing.
Instead of using the crouch-and-sidle type of movement you are used to from stealth in games like Crysis or Deus Ex, what you want to do in EVE is wait for the enemy to turn away, then move rapidly to the next piece of cover.
Eve has some interesting mechanics, like this stealth system, but it seriously lacks any explanation of that. This lack of explanation is a major running annoyance through the game, the "tutorial" is insufficient.