Saioshi no Gikei o Mederu Tame, Nagaiki Shimasu!

Alba was reincarnated as the son of a poor noble. Burdened with a short life expectancy and unable to use magic due to his illness, he is taken in by a ducal family. There, he meets Orcis, his "absolute favorite character" from his previous life. "My fave from my past life is my stepbrother!? This life is too delicious!" ...or so he thought for a brief moment. Alba soon remembers that he is the very reason his beloved stepbrother loses his smile in the original story. To protect Orcis's smile—and to keep admiring him—Alba begins searching for a way to live a long life. From lecturing his stepfather (who was cold to Orcis), to searching for medicinal herbs to cure his own illness, to showering his brother—who has low self-esteem—with praise... As the brother-loving Alba runs around frantically doing all this, Orcis surprisingly starts evolving into a massive doting brother—!? (Source: Alphapolis, edited)