How to frame a bookshelf like this

The Sagulator says it will support about 375 pounds (evenly distributed) before there is noticeable deflection. I recommend you go to the site, read the notes, and play around with the numbers yourself.

Jay's plan to use beam pockets in the front wall will work fine. Dbl. top plates with no additional structure supporting a roof over a SIX foot span (as per Tester101's first suggestion) is entirely inadequate. Whether a 2x beam on edge is adequate, and how deep it is, depends on what the roof snowload is, if any.

There are also hardware beam hangers available that support the end of the beam and are nailed or bolted to the supporting studs in the front wall, eliminating the need to frame pockets. Tester101's second suggestion to use a ledger to support the beam end is a viable idea, but the connection of the ledger under the beam, into the studs needs to be carefully detailed.

A metal plate tying the two walls together is an important detail. Alternately, extend the dbl. top plates over the beam, lowering the beam 3" so the plates can still lap in a conventional manner. If you go with a hardware hanger or a ledger, the beam should be strapped to the sidewall top plate to hold it to the main structure in a wind storm or possibly an earthquake.

Along wind storm lines, be sure the beam is well connected to the outer post, and the post tied into the foundation, as there can be significant uplift forces on an open porch roof.