  The aim of this work is to compare symbolic and ordinary powers of monomial
ideals using commutative algebra and combinatorics. Monomial ideals whose
symbolic and ordinary powers coincide are called Simis ideals. Weighted
monomial ideals are defined by assigning linear weights to monomials. We
examine Simis and normally torsion-free ideals, relate some of the properties
of monomial ideals and weighted monomial ideals, and present an structure
theorem for edge ideals of $d$-uniform clutters whose ideal of covers is Simis
in degree $d$. One of our main results is a combinatorial classification of
when the dual of the edge ideal of a weighted oriented graph is Simis in degree
$2$.
