Should the weight of downvotes be increased?
I think the current voting system has a problem as it causes users to act dishonestly and complicates their decision making process. I will try to explain this in more detail below.
I get annoyed that when I cast a down-vote on a post that I think is bad someone comes and up-votes the post just to make the total zero again, where as if I didn't down-vote the post would remain with zero votes. This means that in these situations between the option of down-voting and not down-voting I have an incentive not to down-vote. This means that I have to guess if someone else is going to counter-vote my down-vote which complicates my decision making process.
The effect of the current design of voting weights is that if someone thinks that a post really has a problem but suspects that another person might disagree he or she has an incentive to act dishonestly and not cast a down-vote:
without the down-vote: the post has 0 total votes, the OP receives 0 reputation.
if the down-voter acts honestly and down-votes (question case) and someone else counter-votes: the question has 0 total votes, the OP receives +3 reputation.
if the down-voter acts honestly and down-votes (answer case) and someone else counter-votes: the answer has 0 total votes, the OP receives +8 reputation, the down-voter receives -1 reputation.
The reputations are small so it might not cause an major noticeable problem. (However I suspect that a few users have got a considerable part of their reputation out of such counter-votes which is annoying.)
It is a bad design of voting mechanism, it causes users to act dishonestly and complicates a user's decision making process (because users have to guess what others think and if there is any other user who would counter-vote). A good voting mechanism should be transparent and encourage users to cast votes honestly based on their own evaluation of the question independent of other user's opinion and votes.
Increasing the weight of a down-vote to -5 or -10 would not completely solve the problem as down-votes still have a negative utility on casters.