Although my discussion of points noted by zengjia shall go beyond the scope of the original posters question, zengjia makes a good point. One could arguably suggest that all E2 elimination reactions should prefer Hoffmann elimination products due to the steric hindrance argument, yet Zaitsev products predominate. I find myself compelled to envision a wider range of reaction timing than the simple models suggested by concerted reactions. A real example that are noted in some textbooks are E2 and E1cb eliminations. Such differences are inferred by an application of the Hammond Postulate or more explicitly stated by Arigoni in analyses of enzyme mechanisms, namely that there are not concerted reactions. That is, if time could be divided into infinitely small portions, then three billiard balls cannot collide at the same time. One ball will always make contact before the other.
If you apply that model, then Zaitsev products can be thought to be E1-like products. That is, if R-X bond cleavage were to begin before proton abstraction, then one might find those electrons best donated to the developing charge should predominate. These will lead to Zaitsev products. If proton abstraction precedes R-X bond cleavage, then Hoffmann-like products should predominate. Because carbons can be thought of as electron donors, then less substitution will be the most acidic, and give Hoffmann products.
In my opinion, most elimination reactions leading to Zaitsev products are in polar solvents, such as ethanol. Note, I am not suggesting a change in mechanism. The rate limiting step is still proton removal. I am merely suggesting that the C-H electrons begin migrating to the back of the R-X bond in a Zaitsev elimination.