The risetime is what will respond to loading changes, and
depending on how you define "delay" you could see up to
50% of that risetime (falltime) as a variable delay adder
(if your definition is based on the output 50% voltage swing
point).
Comparators also have an input overdrive sensitivity which
for slow-moving signals can really push out delay (like a
LM139 specs ~ 1uS for 5mV overdrive but will switch in
100nS if you give it 50mV). Of course most are not this
bad but it's illustrative.