You should first establish the following inequality for n = (p1)^(k1)
... (pr)^(kr):
sig(n)/n < (p1/(p1-1))
... (pr/(pr - 1)).
To do this, begin by writing out the formula for sig(n) as a product of factors involving ( (pi)^(ki + 1) - 1) / (pi - 1). Dividing this product by n in prime factored form allows you to consider factors of the form ( (pi)^(ki + 1) - 1) / (pi)^(ki). Each of these factors can't be any bigger than pi. Why?
Once you've established the inequality discussed, in a new paragraph, turn your attention to the factors p / (p - 1) and q / (q - 1) where p and q are the primes that we're assuming describe the odd perfect n. Since n is perfect, 2 must equal sig(n)/n, which is less than (p / (p - 1))(q / (q - 1)) by the fact above. On the other hand, just how big can these last two factors be? Just how big can their product be? Be sure to prove your estimates. A guess based on consideration of several sample computations does not constitute a proof.