You are basically looking around the $700+ range for a relatively small laptop with a 1920x1080 resolution screen. Examples would be the 11" Lenovo Yoga 3 11 and the 13" Asus ZenBook UX305. Both are 2.6lbs which makes them pretty light, but they only come with a Core M CPU which is more powerful than an Atom series CPU, but less powerful than a Core i3. A 13" Dell Inspiron 13 7000 series starts at above $700 for a Core i5 model and it is a 2-in-1 laptop weighing in at around 3.7lbs.
If you want a 13" laptop that is close to the size of a 11" laptop then there is the Dell XPS 13 which starts at $800 for the Core i3 version while the Core i5 version starts at $1,000. It is pretty light at 2.6lbs.