I have recently purchased a used Trek 7.7 fx and want to install a rear rack. What rack would you suggest. I am looking for a strong but fairly light weight. I can’t imagine ever loading it up with more than 40 lbs. I would appreciate your suggestions.

Back to the dealer and buy one of theirs .. You will know it fits by holding it over the wheel .

I suggest checking to see if you have rack mounts - I don't see them shown or listed on the Trek site.

I picked up a used Cannondale rack from my LBS, I had to make a bracket but its worked out fine...hit your LBS (if you have one) and see what they've got.

You got any idea of what year your bike is? It will be either to codger something on a 2012 or older (aluminum) instead of the carbon of the 2013 and newer frames.

Isn't the 7.7 carbon fiber?

See the post just above yours

Bontrager (Trek's in-house accessory brand) makes a nice "lightweight rack" for road bikes and the like; however, if you do indeed have a carbon 7.7 FX, then it wouldn't be compatible. The current 7.7 FX basically has the same frame as a 3-series Madone road bike, so you might need some sort of rack which clamps onto the stays or something. If your bike is aluminum, on the other hand, then the regular should work fine.

It is a 2013 and yes it is a carbon frame.

Axiom makes one for CF frames:
Streamliner Road DLX « Streamliner Series « Racks « Products « Axiom Performance Gear

You could also use one of these with a rack that mounts to the skewer.

I installed this rear rack on my Trek 'Pilot', which is a carbon bike with a carbon seat post:

Arkel Randonneur Rack - Seat Post Rack - Carbon Seat Post Friendly

Its a sturdy, well engineered rack with plenty of weight capacity for commuting and weekend outings. Its a bit pricy, but most good gear is.