The very fact you're asking these questions means you don't necessarily want to leave, so don't put yourself in the position where you have to if your employer offers less than 1.5. If your employer is sensible any negotiation that uses the phrase "or I leave" will result in you leaving. They will pay you what they believe you are worth to them - any offer you have from someone else is largely irrelevant.

Also, check your contract and the large company's contract very carefully. There's probably a clause that says you shouldn't leave to work for a customer in your contract, and the large company shouldn't approach you with an offer in theirs. Accepting the job could be difficult, and if you leave before checking you'd end up without a job at either company.