Both Uses

assess
in
The Souls of Black Folk
(Edited)

The total assessed property has in this same period risen from eighty thousand dollars in 1875 to two hundred and forty thousand dollars in 1900.
Chpt 8 *

assessed = valuation of (for tax purposes)
Besides this, the system of assessing property in the country districts of Georgia is somewhat antiquated and of uncertain statistical value; there are no assessors, and each man makes a sworn return to a tax-receiver.
Chpt 8

assessing = valuing for tax purposes

Definitions:

(1) (assess as in: assess the situation)
to evaluate (consider something and make one or more judgements)
(2) (assess as in: assess the monetary value)
determine a numeric value of something -- such as a property's value or a truck's weight
(3) (assess as in: assess a fee or penalty)
charge a tax, fine, fee, or penalty
(4) (meaning too rare to warrant focus)