To get the true answer you will need to do some looking at how your trailer is built and how it is supported. So far your guess about the construction is almost certain to be wrong. Nobody would build that flimsy. But to find out, it will take somebody looking underneath and finding out. This is a drawing of what a 14 wide is likely to have in floor support.
You may expect two very large iron beams front to back. the front will be where the hitch was attached for towing down the road. May be there or removed. Locate these two beams and then look for cross beams which may be the 2X6 you mentioned. But they will be spaced more like 16-24" apart and laid across the iron.
How your trailer is set up and supported from the bottom is what determines how much load you can safely hold up. In a trailer, pay little attention to the inside walls as they only set on the floor. Not like a stick built house.
The green areas where it would be over the iron is best as it is fully supported. In between is less as really , really heavy weight could make the wood bow down. The red is the worst as it is farther from support and more prone to bowing. BUT all of this can be changed IF there is support underneath. The red area can be fine IF the outside is placed on a firm foundation or IF there is a pier (jack, beam, etc.) placed underneath at that spot.
The iron beams are likely about 6' apart with only about 4' stuck out to the sides so if you get somewhat close to on top of the iron, all is well.
If you HAVE to stick it on the red spot, lay a couple 2X12 under it and put a jack stand to hold it up.
Life does not have to be difficult, just well thought out>>>>