I can think of one disadvantage to timber framing vs. platform or balloon framing, and that's the need of a crane. Depending on your site, bringing in a crane to install the upper members might be a problem, whereas with stick-built, you're not moving as heavy of pieces, so it's not as much of an issue. (it still might be useful when it comes to roof trusses, though, but it's not necessarily required)
An advantage is that timber-framed structures can span very large areas, so if you like an open design, great rooms, and the like, it's very easy to do. As none of the internal walls need to be load bearing, you can more easily move things around should you need to add a bedroom or remove one down the road.
... but before you built, you might also want to consider comparing to other newer building methods, such as SIPs (structural insulated panels; built off-site, then get craned in and installed in over the course of a few days, so the building envelope isn't open for very long), or ICE (insulated concrete forms; install like blocks, rebar is placed, then you pump in concrete). Both have great thermal characteristics, if you're in a climate that needs it.
With anything that's not platform built, you're also going to want to check with your local permits office -- anything that's not what they're used to dealing with is going to slow things down considerably.
There is no mention where the cut out is but this should take care of it in any respect, as long as the mid span support is a series of posts and not a purlin...
Can you get a 2X6 in there that will give close to a full span? if the material is clean or can be scraped clean, a healthy bead of construction adhesive zig-zagged on the face of the old 2X and screw the 2X6 starting 4 inches from the ends with a pair of screws and 12+/- inches apart in the remainder in pairs also. Use 3 inch drywall screws or 2 3/4 inch SDS screws through the 2X6 into the 2X4. Make sure the screws draw tight the material, pilot if needed with a 3/16" bit.
If you have a mid span support that goes to good bearing through to the foundation, you can use a shorter repair joist, but a single joist that goes over multiple spans is stronger than a single span joist.
FWIW, it looks like a 2X4 will suffice from what I seen the table at page 396 of the 2012 building code (table R802.5.1).
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In Canada, while officially we are metric, all the construction work I've been around is done almost entirely in imperial. Everything comes in the same dimensions, and is referred to in feet and inches. Framing is done 16 or 24" on center, standard ceilings are 8' high.
Part of this may just be a hold-over from years of everyone doing that way, and then passing that on as they teach younger tradespeople. In school, I grew up learning the metric system, with the most exposure to feet/inches while doing fractions in math class.
I think part of it has to do with convenience and standardization as well: a "1.22 x 2.44m plywood" is awkward to say, and changing the dimensions slightly to 1.25 x 2.5 m would be strange. 16" (0.406m) centers is about the right distance for drywall, and so if you had 1.25m sheets of drywall, your centers would have to be 0.416m (or 16.4") to work out.. that's awkward to deal with.
Personally, I use a tape measure that has both centimeters and feet/inches on it, and often use cm if I'm measuring any more accurately than 1/8". One thing imperial has going for it, is the foot is a very handy size. There is no equivalent in metric (the decimeter (10cm / 0.1m / 3.9") is too small (plus no one ever says the word "decimeter"), while the meter (3.28ft) is too big).