Barring health issues or other extreme mitigating circumstances, a woman over the age of 35 without children almost certainly possesses a range of personality traits and/or life experiences that make her wholly unsuitable as a partner. In a nutshell, she's either extremely selfish, extremely short-sighted or extremely stupid. She's also very likely to be heavily emotionally scarred by her previous failed relationships.
The one woman I really got to know off a dating site recently is 40 without children (I'm 39, also childless). She is very beautiful (she looks like Jessica Chastain), and is likewise a bit obsessed with physical appearance - her own and others. We still get coffee and chat, although I'm not holding my breath.
Anyway, I think she is a decent woman but the main thing with her is that as a single woman for so long, she has received (and continues to receive) lots and lots of attention and validation from different men. And that is maybe her biggest weakness - would she be able to shut all that validation down and be satisfied with just one man's attention and love? It's hard to say. But in asking that question, I turned it back on myself and realized that is also my biggest question mark - as an unmarried man for my entire life, could I be satisfied with just one woman? And ultimately it's the more important question as I'm the only person that I can control.
Lastly, we both have to realize that just because a person of the opposite sex wants to sleep with you, doesn't mean that person wants to marry you (leaving aside whether it would even be a good marriage). Both of us have become addicted to validation from the opposite sex, but I think her, more than myself, mistakenly equates the attention she receives to her actual marital value. I think she believes she would be "settling" on me.