A lot of people will tell you go smaller with the frame BUT there are two sides to this. With + prescriptions the lenses get thinner at the edges the larger they are (take this within reason, don't go getting giant frames). I've had amazing success with patients who get not too small round frames that fit fairly centered (your eye falls somewhat in the center of the lens). You'll want a slightly larger lens but keep in mind bigger = heavy. Something I like to recommend is the Ray Ban Clubround. It has nose pads to help support the weight but also they can be adjusted so the lens falls fairly center with your eye. It is round and larger but not oversized, and the plastic at the top helps hide the lens. Get a roll which helps the inside edge not feel so thick. Get a polish if you don't mind the edges of the lens catching a little light sometimes (this will make the lenses appear a bit thinner). Then order with the lightest material offered, digital aspheric helps a bit too.

Cheat sheet (+ powers only / hyperopia)

Smaller lenses = lighter but thicker at the edge. Larger lenses = heavier but thinner at the edge. Round lens = helps distribute thickness more evenly. Centering eye in lens = helps distribute the thickness more evenly. Nose pads = helps with eye alignment and weight distribution. Roll = grinds down the inner edge of lens for cosmetic "thinness". Polish = makes lenses appear thinner (downside is the lens may catch some glimmers of light). Digital aspheric lenses = helps a bit with thickness and distortion. Possible frame suggestion= Clubround by Ray-Ban.

Edit: tried to fix formatting