Puzzle #48: Weights

You have a balance scale with two pans. You have a set of five weights. You wish to weigh objects that weigh an integer number of grams.

Solve these scenarios:

1) If you put the object in the left pan and put weights in the right pan, what is the weight of the heaviest object that can be weighed, and what are the weights of the five weights?

2) Like #1, but you can put weights in either or both pans.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, May 7, 2014 at noon Pacific Time. I will post the answer shortly after.