Oniisan
WARNING!: Contains spoilers for mangas 2, 4, and 11 :D; If you haven't read these yet and want to, um...read at your best discretion~ Much of this is my interpretation!
Tatsuha and Eiri...or rather, Eiri and Tatsuha because Eiri is older. These two are an interesting pair, and here's my take on their relationship.
Firstly, they're nearly identical in appearance, which the few obvious differences - hair and eye color (Tatsuha has very dark eyes that are almost bluish in the anime O.o And dark hair. Eiri, uh, doesn't?). Tatsuha is also shorter by...two centimeters, whohoo! Which means he may be taller when he's older :D 'cause boys do not stop growing at sixteen, nope~ They are also seven years apart.
Okay, basics out of the way, here's how I view their relationship - brotherly love and friendship twisted because of idealism. Fwee! Trying to put that short is hard, but I'll explain more...
When we first meet Tatsuha in the manga, Shuichi notices that Eiri and Tatsuha seem to get along pretty well and are friends. Eiri then tells Shuichi that Tatsuha has been the only person not to treat him differently because of how he looks. We can assume this goes back to childhood as well, when Eiri got picked on. Many fanfic writers like to write Tatsuha as standing up for his brother, though much older than he, or threatening other kids and such for messing with his big bro :D
Despite this, Tatsuha does idolize Eiri. Whether this is because of a little brother complex or just because Eiri is Eiri, he does, and says so in book 11. However, the Eiri that Tatsuha knew changed after going to New York. Eiri was 16, Tatsuha was 9 at the time. I like to think that Tatsuha considered Eiri his best friend, not only his big brother, and seeing that personality change to one much more moody, recluse, and someone who really didn't want to be around their family, well...Imagine what that would be like for a 9 year-old boy?
We're not sure when Eiri or Tatsuha started to get into that more 'dark adult' side of life - meaning drugs, sex, and rock and roll? well, you know ^_^; - but it's safe to assume Eiri started first. Tatsuha does idolize him, and I think that seeing his older brother starting to do things like that is what got Tatsuha to as well. Whether it was because he wanted to be like his brother, find ways to spend time with his brother, or prove that he's adult enough to be worthy of his brother, we don't really know. I like to think it's all of the above - a kid brother wanting acceptance from someone he looks up to so much.
Also note that because of Eiri, the duty of taking over the temple has been passed down to Tatsuha. It's clear in the manga (book 4) that Papa Uesugi would much rather have Eiri come back and take it on, but Eiri's not necessarily jumping up at the opportunity. But what does that leave Tatsuha? If you think about it, suddenly his entire life is turned upside down with new responsibilities and his future is set out for him, all thanks to Eiri. But, we don't really see Tatsuha being resentful of it, which is what surprises me. He doesn't seem like he's excited or anything, but maybe that he's at least resigned to it, or doesn't blame Eiri. It depends on your take~
And that leads to the current story-line in Gravitation :D While they're not ready to hug and jump and spend quality time with one another, they do clearly get along rather well. Okay, Tatsuha did kidnap Eiri and Eiri has kicked Tatsuha out before, but they do love each other, I'm sure! Hell, Eiri trusts Tatsuha to look after his apartment while he's out of town and what not, right?
See? Brotherly love ^_^