Situation; A few years ago bad weather all over the London TMA, Heathrow easterly operations. All and sundry stating that the weather was showing very heavy in the approach funnel and nobody wanted to fly an approach, therefore zero landing rate. Wind was too strong to consider changing ends (which would have meant departures getting airborne into it). Aircraft in the holds were then asking for EATS!!!!!!! (with zero landing rate and no one prepared to fly an approach, crystal ball required).
If aircraft can't fly the optimum routes (understandably) capacity will be adversely affected.
Monday evening, Heathrow again easterly operations. VIR 340 airborne on CPT departure asked for heading 300degs as soon as airborne. Slow climbing aircraft requesting a heading that would put it straight into confliction with all of the traffic on the final approach on 09L!!!!!!
We will do our very best to accommodate requests to avoid weather, regrettably occasionally the answer has to be no.