One thing I've heard Richard say in interviews was that Karen's anorexia started in 1975. But I think the obsessive thoughts started in 1974 even if the effects did not show yet. Clearly watching clips of Karen in 1974, she looks wonderful. Towards the end of 1974, she looks noticeable thinner (see the Perry Como Christmas special), but she doesn't look ill. But in 1975 especially near the end of the year, it is very clear she had gone too far with the 'dieting'.
Again, while she starts to look ill in 1975, the thoughts and the obsessions started in 1974. You just don't get that skinny overnight. 1974 was their peak. The Carpenters were everywhere. They had number one hits. So clearly, it wasn't the declining popularity (which eventually happened) that caused Karen to slip. She was also still very young, so I don't think the lack of a romance was a problem also.
I think it originally started with a simple desire to look thinner. She was a performer, removed from 'hiding' behind her beloved drums. In retrospect, we look at those videos from 1974 like the Budokon Japan concert or the one in Holland and can revel in how healthy she looked. But she wouldn't have been considered 'thin' by society's standards, maybe average, certainly not fat.
I think she particularly was frustrated with her hips. As Richard has said, she had her bone structure going against her. She just had bone structure that made her hips wider than say someone like Olivia Newton-John. Even at her thinnest, her body below her waist could be deceiving when she was wearing pants. If you saw her face it was a give away. Mostly Karen wore pants and jackets in her later years. You primary saw the anorexia effects in her face.
So my theory is that she originally got obsessed over something she had absolutely no control over, her hips. She then did take the diet too far. The 'dieting' soon became a learned behavior. She discovered this high that she got from feeling her bones and being thin. So when life got difficult, or she was not happy with something (Richard's girlfriends, declining sales, feeling like she was betraying Richard with the solo album, her mother's lack of attention, the marriage, etc.), she turned back to her addiction, anorexia. That was how she learned to deal with life. She didn't resort to alcohol, or other substances, she fell back on this 'good girl's' addiction. But just like all other addictions, the reason to turn to it are all the same.