One of mine cried all the time (and has started again approaching 9 - teenage tantrums already, apparently).
She wasn't unhappy, just hated sleeping, would cry if I left her room (literally used to creep out when she was asleep, then floorboards creaked, eyes opened, and all hell broke loose). She'd wake again at 2am, then up at 6am. It was a phase, it passed, but when I was too whacked to keep my eyes open she cried, then my neighbours banged on the wall, so I had to try to stay awake and entertain her.
My other neighbour, an older woman, was very concerned a few years ago though. I'd gone to psychology session, and left DD with her dad (school hols). DD was going through an unexpected clingy stage, and she cried as she didn't want me to leave, ran up the path (so DH got her in and put the chain on). She got my DH who found my neighbour calling her through the letterbox, asking her to open the door.
Turned out she hadn't realised DH was in, so thought I'd left her alone. I was instantly grateful someone was looking out for her, then 
that she thought I'd ever leave a young child alone!
New neighbours have a baby that cries all the time. I remember it well, and know it's 'normal' and nothing concerning.
Three year olds can be little horrors (and can try the patience of a saint, never mind a parent), but if you think the crying is in fear (and they do sound quite different - or could stop all together, as abused children can be unusually quiet), then call SS.
I'd think the better solution would be to try to befriend the mother. Age/class/interests aside, she's seems friendly you said, so maybe try to engage her a bit. People of all ages, classes and creeds can and are friends, so reaching out would give a better perspective (and ignore the BF, you're not befriending him).