Why are some modern military trainer aircraft so bulky?
You mentioned the oversized canopy for two, staggered for better visibility, and really that is the main feature that stands out.  Consider that trainers are typically quite a bit smaller than their full combat brethren and this feature is even more out of proportion.  Also, full sized combat 2 seaters generally have a Weapon System Officer in the back seat, so good forward visibility isn't as crucial as it is in a pilot trainer so less upward stagger of the back seat is needed.
The human body doesn't scale up and down like an airplane design, it is the constant that must be designed around. Think about it, you are fitting two 6 foot tall people in a fairly small plane vs often one in a larger plane; naturally the space for the bodies will be a much larger overall percentage of the size of the  trainer.
If you were to compare a 2 seat trainer next to a larger 2 seat combat aircraft like the F14 Tomcat, (with its huge engines...) I think you would find that the cockpit areas are actually pretty similar in size.  They are just more pronounced in the smaller plane.
Other than the cockpit area they really aren't &quot;bulky&quot; at all.  In fact the two pictured are VERY compact and streamlined, by just about any standard.