Value of The Popular Encyclopedia?

Antique books (over 100 years old) can be collectible but usually if collectable as an antique they were probably collectible when they were less than 100 years old.
Your set may be an exception since it is about 125 years old - but - the fact still remains true - if it is not a desirable/collectible book/set then it really may not matter how old it is as just being old is not a value.

Pictures can be deceiving but your set does appear to be in fairly good condition.
But, when you are talking about even $100s your opinion of good condition may not match the definition of good to someone who is thinking about paying that $100.When you are asking several hundred/thousand dollars for a book/set then it will be critical as to the true condition.

Several things can affect the condition: dry/brittle paper, loose binding when opened, faded covers/pages, cover material, insect damaged paper (silverfish, book-lice), folded page corners, creased pages, etc.
Usually, a true collector will ask for a verified certificate/appraisal about the set before they will pay this kind of money.

You do not say where you are located but it seems this particular encyclopedia is more popular in the UK than in the US. I did find one set listed for sale on eBay.UK.
This set - from pictures - does appears to be more worn/used than your set, but?

Asking price: GBP $195.00/US$257 plus high shipping.

www.ebay.com/.../233457792470?hash=item365b2b35d6...

www.ebay.ie/.../233457792470?hash=item365b2b35d6...

I did see a couple of individual volumes listed for sale at $25 each but found no evidence of any being sold.

You may be able to use this set as a 'value' to give you some idea of where to start but since I do not know where you live, I'm not sure where you should list your set.

US has several good sites that are probably available in the UK also - Craigslist, Facebook Marketplace, letgo, offeup, etc.
You can always list them with a high starting price - $400 or so - with best offer considered. These books are heavy but media mail is about 1/4 the cost of regular mail (US).
If no one makes an offer you can lower the price when you deem necessary.
You will need a lot of good pictures of full set - front, backs, spines, as well as inside pages/publication page.
You can use these pictures and post them on this site and maybe find out a little more about your set.

instappraisal.com/

In the UK there is a site called Abe Books who has a set of 14 Popular encyclopediae by Charles Annandale that was published in 1901 that they are asking 110.35 pounds for the set. There are many people who are trying to sell off different sets of encyclopedias right now on eBay. Some have a very reasonable asking price for the set of boos and some are listed extremely high. It appears that people's prices range from $150 to over $900 for a set of encyclopedias.

The most reasonable price I did see was from Abe Books in the UK. I'd like to suggest that maybe you go and talk with a book dealer in your area, have them examine the books, and help you determine the real value of these books. A lot of people can tell you that they are very valuable when in some cases they aren't that valuable at all. An antique bookseller will know if this set is really worth a lot of money or only a hundred dollars or so.