Growing tobacco under a canopy of shade cloth causes the plants to grow taller, and the leaves to grow much larger and thinner. This is used for production of thin cigar wrapper. (The total weight of tobacco leaf per plant appears to change little.)
Growing tobacco beneath a shade tree may or may not work out well. The extensive root system of a tree (usually estimated to extend as far out from the trunk as the widest part of the upper tree) may draw away sufficient moisture and nutrients from the soil to severely stunt the growth of the tobacco grown within its shade. On the other hand, if you have taller, more distant trees that provide substantial shade to the tobacco during much of the day, the results may be worth the effort.
Bob