Commenting on the muscle imbalance problem - you could have contracture of the biceps/brachialis muscles but in a healthy individual who did weights i would have thought that unlikely buit not impossible. If your weight training was excessively oriented to exs like preacher curls and backward rows at the expense of triceps strengthening exs it is possible. However almost all weight programmes include a smattering of exs that include the strengthening of triceps: bench press, dips, shoulder raises etc. Guys often go mad over building up biceps because they think it will make them look more massive in the arms. But even if the elbow flexors are overly developed you should still manage to extend the elbows using your muscles.
An important alternative is that you have lost range of motion at the elbow joint itself. Possibly cumulative trauma to the joint is a possibility. this could even be the start of degenerative changes in elbow joints. However this would more likely be more noticeable on one rather than both.
the best way of testing this is to have someone passively stretch your elbows into extension and feel what the end of the range feels like. If there is a gradual increase in resistance with a springy end feel that usually suggests muscles where as if there is a much sharper end to the movement or a bony end feel that suggests the joint
A final option (if your elbows have always been like this) is that there is nothing wrong! You just happen to be someone who has hypomobile elbow joints. You may just be an extreme example of the normal variation of joint mobility
I would get an opinion from a MSK physio - a bit hard to comment over the internet.