Client want source code but their project will use a big code base

The first thing to keep in mind is that source code has value separate from the binaries. It is perfectly reasonable to either refuse to sign a contract that requires source code delivery, or to insist on extra payments for source code delivery. Contracts are two-way documents. Do not let the other part dictate what is required just because they are "big companies" and "do this all the time". First, decide what you are willing to deliver and how you want to be compensated. Then take their contract to a lawyer and work out what needs to change. Then, you negotiate.

Don't do what a lot of young people do when they start contracting. Don't just sign because it seems like they have lots of experience and you don't. That's a good way to get ripped off.

Look into why they want the source. They may want it so they have the option of using another developer later on. Or they may want it just because they are afraid you might get hit by a bus and suddenly they'll be left with binaries that they cannot improve. If it is this second case, look into a Software Code Escrow Service. These services hold the source code in case you go bankrupt or otherwise are unable to maintain the software. This may satisfy both your desire to keep your code proprietary to service other customers and their desire not to be left holding the bag with an unmaintainable set of binaries if something bad happens.

Remember that any source code requires a license. If you hand over source code, the company can use the source code to do anything that the license allows, and anything beyond that is copyright infringement. So if you hand over source code, you would have a contract that makes absolutely clear that you retain the exclusive copyright of the source code, and exactly what uses of the source code are allowed. And of course source code + license wouldn't come for free.

A major company would be unlikely to infringe your copyright, because being caught would cause a major damage to their reputation, apart from financial damage. On the other hand, paying out for software with no guarantee that any problems can be fixed in the future, might be unacceptable for the client.

The way to deal with this is to negotiate.

If they want source code, then they should be prepared to pay for it, and it is up to you to decide how much that should be.

On the other hand ... if they are not prepared to pay what you want, they may "take their business elsewhere".

Welcome to the world of business :-)

And when you talk to prospective customers in the future, be sure to mention this issue early on ... to avoid wasting everyones' time.

It is also worth noting that what you are doing is anathema for open source developers, and for (educated) customers who are looking for open source solutions.

Your question is, what is the best way to circumvent this issue? But what do you see as the issue? Others have correctly pointed out that it's a matter of negotiation: everthing has a value, and it's up to you give the client a price for providing what's asked for.

But you must also carefully consider—and write into the contract—the implications of providing the code. Is it just so the client can see it? Can the client modify it? And in particular, would you consider giving your client exclusive rights to the code base you have created over the years and is used as a template for most applications so that you can never again use it yourself in the future?

You need to ensure the contract explicitly states who has rights to use the code, and in what ways.

"No" is a perfectly fine answer, actually it's an incredibly useful answer which for some reason I can't understand is very underrated.

"Hi, we have suddently decided we just want source code too, free of charge."
"Hi, no."

It's not that difficult, really.

Then, if they wish to pay egregious amounts of money over what they already owe you, you might give them a trimmed version of your application, which includes only the sources they actually need, and taking care they get absolutely non-exclusive rights.

Don't complicate simple things.