The other answers have touched on pieces of the puzzle, but the high level view is this: All of security boils down to risk assessment, risk management, and risk mitigation.
Because of this, there is no generic answer for your question. Here are some of the sorts of things you need to look at to determine whether or not this practice is acceptable in your environment.
Do you control who has access to the system? (You do in this case, since you mentioned users need network access.)
Who has access to the system? (Enumerating the users who could potentially access the system will give you a better idea of the exposure.)
Do you trust these people? (This is going to be subjective, rather than objective, but it makes it an easy decision if the answer is "No.")
What damage could be done if the system is abused? (If someone adds, edits, deletes, or steals data from the system, what is the cost? Is the data valuable, and could a salesperson who has access to the system be tempted to take it with him when he leaves the job, for instance? Or perhaps the systems contain nothing of value and can be easily and automatically re-based to a known good state.)
What is the risk of the system being abused? (Still subjective, but based on what you know about the system and the users, what are the chances that someone might try to maliciously access the system?
What is the cost of mitigating the risk? (In this case, mitigation is going to involve implementing a good password policy. Is that going to cause additional work for the developers?)
Once you've analyzed the risks to your systems, you can now make a quality, informed decision about whether there are risks that are worth the bit of extra effort to mitigate. If the risks are extremely low, as is not impossible to imagine for an internal development environment, it may not be worth it to make the developers lives even a little bit harder. If there's sensitive data involved however, or a malicious attack on one of your applications would have a significant cost to recover some and the likelihood of such an attack is non-negligible, than it's likely that the small additional effort required for strong passwords may be worth that cost.