Scientific studies are few but the only proven relationship between bulb weight and fertilisation, is when nitrogen is given. Potash and phosphates have their place in stimulating rooting, flowering and fruiting but they do not make the bulbs larger. Think about it - it makes sense. Tubers are lifted and cleaned or repotted each year. Diseases and pests are few.
Pests are usually obvious, slugs, rodents etc.
Fungal diseases are best prevented by dipping in systemic fungicide when symptoms are noted. Symptoms include rotting, oozing of variously coloured mucilages and premature dormancy, although very high temperatures can trigger dormancy in healthy plants. Plunging potted plants in compost or sand will help to even out extremes of temperature and water levels and provide a degree of resistance to frost. Even unheated air circulation will give you another 4 degrees of frost protection under cold glass. I have little or no experience with tropical species however Tony Hall, grower par excellence at Kew advises that they are best in a totally frost-free glasshouse.