A number of pairs have in recent times decided not to come to our weekends.

Some have said that four sessions of bridge has become too much, which I understand, but at a bridge weekend we always play four sessions.
There is little I can do about it.

However, at least two other pairs want to come but have become disillusioned at not feeling part of the competition.
I can understand this - we all play at different levels.
But I can do something about this, and that's by introducing a handicap system.

This doesn't mean the results are random - it means that those pairs that play above their personal averages will be near the top.

That can't be a bad thing.

BridgeWebs calculates every players average after every session.  You probably look for yours under Player Statistics / 2024 Individual.
For the purpose of handicaps it uses the average at the beginning of the month.

If the players in a partnership have averages of 44% and 46%, their partnership average would be 45%.
BridgeScore would give them a handicap of +5%.
This 5% would be added to the score they achieved during each session.

So if they scored their exact average, 45%, their score for the competition would be 50% (45% + 5% handicap). 
But if they scored above their average, say 49%, their published score would be 54%, somewhere near the top of the leaderboard.

Conversely, a good pair with an average of 55% would get a negative handicap of -5%, so would have to beat 55% to get a good result.

Basically it means that every pair has to play above their average to be at the top of the leaderboard.