If ewes are in optimal condition, once passed the 1st cycle of mating, they do not need to continue to be gaining weight. The excess of grass around this year means it will take proactive management not to allow breeding ewes to gain weight in the 1st trimester. May to June is an opportune time to tidy up poorer quality paddocks or even feed-out 2nd year baleage to conserve green feed for later pregnancy.
I do not like to discourage farmers from feeding stock well, but there is some evidence showing that there is an increased bearing risk with weight gain through this period. Yes lamb birth weight is affected by feeding levels at every stage of gestation, so it makes sense to save better quality and quantity of feed for twin bearing ewes after scanning.
Body Condition Scoring
BCS and feed budgeting is the way to take the guess-work out of this subject. I expect more ewes should be in better than BCS 3 this mating and will be scanning well this year. The next bit is to set them up for optimising lamb birth weight and survival without getting them stuck upside down cast or poking their back-end's out.
If there are lighter BCS ewes, then taking them out early for preferential treatment makes it possible to "re-build" condition from now to the point of lambing. Adding BCS to light twinning ewes after scanning and shearing is hard to do with the bigger foetus taking a greater part of reserves.
The recommendation is slightly different for ewe hoggets. These need to keep gaining body weight through mating and early pregnancy, ideally 4kg per month from now to the end of June should see a standard cross-bred hogget reach ~50kg.