I don't think that little bit of weight would create that problem. I think you have 2 issues, the spring is one and needs to be fixed, and the narrow stance of your wheels can be a problem on some roads. There is usually a hump or ridge created in the middle of most roads cause by heavier vechicals running in the same groves over time. That trailer is running inside those groves. One tire will catch that ridge and try to climb it the it will do the same thing on the other side causing the wag back and forth. Without the motor you probably just never noticed it but even though I said it didn't make a difference maybe just that little bit agrivated it. But I'm thinking combination of narrow stance and missing spring.
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Charlie Weaver USN/ENC 1965-1979