I regularly pull the road train consisting of the trail-a-bike with my 6 year old attached to my LHT, and the kiddicarrier with my 3 and 2 yr olds plus all their stuff for a day out attached to the trail-a-bike, (well over 100lb in tow) up a couple of miles of 4% - 6% incline with my 16 gear inch granny, easy. You can climb anything in you have low enough gearing, enough traction, and just enough forward motion to stay upright.

I suggest you get your trailer and do a small shopping load first, say 10lb at most, and see how you go.
Also, towing weights uphill is really good for you. It makes your legs bigger and stronger. This becomes very apparent when I ride with my weekend-warrior roadie friends on my 16lb Cannondale and have to wait for them at the top of every single hill.