My Connie is a full up 14.2, in a 5ft9 rug and in a cob/full size bridle, same as my 14.3 Welsh x Arab, was and same near enough to my 15hh Appy x Criollo (She's in a 6ft rug). My mum and I are 5ft4/5 and about your weight, so I wouldn't rule them out as being small ponies. I've seen Connies up to 15hh as well, and they are pretty cheap and plentiful over here.
My Storm is 15hh and a connie, she'd carry @Jessey just fine.