My three week old starts getting fussy in the afternoon through night time. What could cause this?

Colic. Babies can have fussy time in the afternoon thru evening from 2 weeks of age thru about 8 weeks. It is a normal but difficult time period of fussy belly and hence fussy baby. Try some skin to skin time as this often will soothe baby. If you get anxious or angry, put baby down in the crib for a while. Baby can cry alone for a few minutes until you feel under control again.