On the weights of Boolean functions representable by $2$-CNF or $3$-CNF

Sets of possible values of weights of bijunctive Boolean functions ($2$-CNF) are found. For Boolean functions having all variables as essential ones we describe: sets of bijunctive functions with weight close (but not equal) to the maximal value and sets of functions of maximal weight represented as $3$-CNF. A hypothesis on the maximal weight of functions representable as $k$-CNF ($k \geqslant 4$) and having all variables as essential ones is formulated. Some sets of balanced Boolean functions representable as $k$-CNF are described.