The weight adds up quickly. The only place I have any stud lumber in my build is the blocking for the side door latches, and the blocking for where the floor bolts to the trailer frame, maybe 2 or 3 ft total.
I suggest you start at the very beginning with a mind set of making everything just 10/ct heavier than "this is too weak", instead of 200/ct heavier than BMFH (Big Mother Freakin' Hammer).
Sure it's more effort to find, buy and/or rip down suitably sized sticks, but of all of the stud lumber builds we have seen, not a one has said, "I wish I had built heavier". On the contrary, we have seen broken tongues, broken springs, and maybe even a bent axle (IIRC).
Have a look at
Sharon's finished build weight comparison chart (and a companion thread
http://tnttt.com/viewtopic.php?t=60392). Take a look at the campers of similar size to what you have planned and look at their build journals to see the type of construction they used. The campers outlying the graph on the heavy end of the plot (for a given floor size) will be those that overbuilt using stud lumber (and possibly lots of extra features, such as onboard water, a/c, generators, solar panels, extra batteries, etc.); whereas the ones in the "sweet spot" of the plot used more commonly used materials and methods, with some restraint of features, to keep things at a more manageable weight.
Remember, even if your TV has all the pulling power you could ever need, your hauling experience will be better when the actual finished weight is less, and especially when that finished weight matches the axle, spring and tires you have selected. There are plenty of examples of people that ending up heavy and wishing they had not started with stud lumber.
As they say, "think airplane, not tank".