The equivalent weight of HNO3 in the following reaction
The term equivalent weight is used in conjuction with normality (which is quite obsolete, except in the industry). Anyway, whenever you determine equivalent weight, you have to know beforehand whether you are considering a given "molecule" as an acid or as an reducing/oxidizing agent. This is where the confusion sets in.

Nitric acid as an acid is a monoprotic acid: It's equivalent weight is the same as its formula weight

Calculating the equivalent weight of nitric acid as an oxidizing agent is another story, it depends on how the redox equation is written.

From your equation nitric acid is acting as an oxidizing agent because there is no nitrate ion on the right hand side and the oxidation state of N is different on both sides:

$\ce{HNO3}$ is converting to NO. In the answer above, you already have the equation

$\ce{ NO3−}$ +3e => NO 

In this case, the equivalent weight of nitric acid is 1/3 (formula weight).

As you can see equivalent weight is very much dependent on the way you write the equation. This will come with practice.