I became anaemic in my 3rd trimester last pregnancy and had a large amount of blood loss which could have been due to my emergency c/s or anaemia. I was on iron supplements & vitamen c, and yes it did cause constipation too... Matilda was 8lg 15oz so I'm not entirely sure about the low birth weight thing, but hey she may have been bigger had I not had anaemia LOL.... Taking the iron consistently led to me having more energy & being able to continue things like walking etc.