Week 1: your period happens, last approx. 5 days
Week 2; the week after that
Week 3: ovulation and potential fertilization
Week 4: fertilized egg implants in uterus 6-10 days after fertilization (~1/2 don't implant)
Week 5: fertilized cells form embryo, <1/5"
Week 6: basic heart and circulatory system develop
Week 7: embryo now 1/4 - 1/2" long, sex still undifferentiated, not yet male or female
Week 8: sex may be set, eyes and ears begin to form as well as arm and leg buds
The "average" woman expects her next period 28 days from the first day of her last period. Any number of things can cause a woman to be "late," and many woman aren't "regular." So the "average" woman is wondering what's up, if anything, at 5 weeks. Irregular woman may not suspect anything even at 6-8 weeks. This is the magic moment that (the men) in MO define as the last moment termination of pregnancy can happen. That gives a woman 0-3 weeks in which to 1) suspect they may be pregnant and 2) make a decision on whether to continue it or abort, and 3) make an appointment to confirm a pregnancy and schedule a procedure. If the care center is far from home and the woman has other obligations in life - work, school, exams, kids - this timeline can be near impossible, which I guess was the point.
That microscopic heart was beating at 5-6 weeks. Why not set that as the deadline? Because no woman knows for sure she's pregnant then? "Heh, heh, let's make the deadline 5 weeks! Adequate pre-natal care? That's the slut's problem. Support after the baby is born? Again this is the responsibility of the mother, if she can't afford it, well she should have thought about it sooner." MO must be an ugly place to live if you're female.