Not if the 'baby' will cause harm to the mother or be born with defects.
The number of abortions performed after that stage of pregnancy is vanishingly small, and would almost always be because of serious abnormalities or risks, not just because the pregnant woman has randomly decided she can't be arsed having a baby.
Generally, a pregnant woman in the UK will have two ultrasound scans - one at about twelve weeks, which dates the pregnancy and screens for the likelihood of some problems, and another at twenty weeks, which is a detailed anatomy scan. Many conditions would only be observable at this second scan, and often further scans or investigations would be necessary to confirm the diagnosis. So, for example, a woman might be told at twenty weeks that it's likely the foetus she's carrying won't survive for more than a few days/hours after birth, and that it would be in significant pain for the duration of its short life - and confirming this diagnosis could take another couple of weeks. In those circumstances, I can absolutely understand why she might choose to terminate the pregnancy.
Incidentally, being 'three weeks' pregnant is not really a thing. The way pregnancy dates are calculated, you're considered two weeks pregnant at the moment of conception, and the embryo doesn't implant into the uterine wall for another week (or more) after that, with a further delay of a few days until the resulting hormonal changes can be detected by even the most sensitive pregnancy tests. So, a woman who is three weeks pregnant literally cannot know at that point that she's pregnant in the first place.
I believe abortion should be allowed up to 3 months after birth. It gives the mother time to decide whether she likes the choice she has made
My (admittedly stupid) question, is why, unless due to medical complications, would a mother choose to abort after 6 months?