Fitting the biggest possible tire is very sound advise. However, given that you've already broken a few spokes on the rear, others will probaly be breaking in the near future, so I'd be considering a new rear wheel. The more spokes, the stronger the rear wheel. You will want at least 36 and may want to consider a 40 spoke grand touring wheel. Heavier gauge spokes of top grade will also help. The other big factor is rim design. A box section rim is much stronger than a open section rim, though there are few to select from in 27". Consequently, you may want to consider a 700C rim if you have sufficient brake reach. However, the most important factor is proper spoke tension. This can vary quite a bit on pre-built rims and I'd seriously consider getting a wheel built by an LBS with a good wheel building reputation. It will definitely cost more but in my experience is worth it. They will also be in the best position to advise you on the correct wheel for your particular application.