Light economy fare baggage on KLM booked through Delta

No specific knowledge or experience, but I'd note that your carry-on just barely exceeds the limit - by one inch in length. It's not like KLM or any other airline measures carry-ons before or as passengers board!. They don't even make people use the sizing thingies at the gates that allegedly show you if your bag is too big. More generally, I'm always amazed at passengers' flagrant carry-on abuse. There is no enforcement. IMO you have nothing to worry about.

I found the KLM rules online:
https://www.klm.com/travel/us_en/prepare_for_travel/baggage/baggage_allowance/index.htm

They state in the "General included check-in baggage allowance" section for "Economy Class on European and intercontinental flights" that

** The Light ticket option does not include check-in baggage.*

It doesn't say how much it will cost to check a bag, but the "My Trip" link in this section should tell you:

The actual baggage allowance can differ per flight. That’s why we show you the exact baggage details for your trip on several moments: when you’re booking, in your booking confirmation, on your ticket and in My Trip.

Typically I've seen 60 Euros to pay for a first checked bag, but that varies with airline and flight route.

My experience in Europe has been that gate checkers will ask patrons to confirm that their bags fit within their "sizers" …. especially if the flight is close to capacity.

Well, you were provided the criteria when you bought the ticket so you have to decide what it is worth to you. Some people sail right through with no measuring, others have to do the frame test. If you know your luggage is too big, what's it worth to you? If we use the 60 euro figure, you can get a smaller, lighter carry on and take a bigger personal item that complies and then you don't have to worry about it for now or future travels. There is no valid answer as it depends on the day, the airport, the airline, the type/size of plane, the mood of the staff on that given day. You can't control any of those, but you can control your luggage size.

I don't know if Delta/KLM has a similar deal, but I bought United economy-light using a United Mileage Plus credit card and got one free checked bag.

My main concern would be the flight from Brussels to Amsterdam and the size of the overhead bin. It looks like the aircraft will be an Embraer E-190. You might want to find out whether your cabin bag will fit in that size aircraft's overhead. Also, because it is a smaller plane, the gate agents may be more picky about cabin baggage.

It can also depend on what plane model your flight from Brussels is and how full the flight is. The smaller planes used for short hops can have very tight overhead space. We flew Delta/KLM SLC to Amsterdam then a hop from there to Budapest. On the Budapest leg the flight was full and the plane small so the gate agents were looking hard at any carry one that might not fit and gate checking them. You should be fine on the transatlantic legs.